The phrase to snatch victory from the jaws of defeat, and its variants, mean: to win a battle, contest, etc., when defeat seemed inevitable.

The phrase to snatch victory from the jaws of defeat occurs, for example, in the column Inside Westminster, by Andrew Grice, published in The Independent (London, England) of Saturday 9^th May 2015:

The history books may record that the seeds of David Cameron’s remarkable election victory were planted at 7am on 19 September last year.
Two hours after the result of the referendum on Scottish independence, he promised “English votes for English laws” to ensure that the Conservatives rather than Ukip could play the English card.
His opportunist move was not part of a cunning general election plan but helped the Scottish National Party snatch an incredible general election victory from the jaws of defeat in the independence referendum. By saying that “English votes for English laws” would run in tandem with further devolution to Scotland, Cameron played into the SNP’s hands, giving it a new grievance.

Conversely, the humorous phrase to snatch defeat from the jaws of victory, and its variants, mean: to be defeated in a battle, contest, etc., when victory seemed inevitable.

The phrase to snatch defeat from the jaws of victory occurs, for example, in the following from This senseless lawsuit could bankrupt the Labour party and let the Tories win again, by the British author George Monbiot (born 1963), published in The Guardian (London and Manchester, England) of Wednesday 15^th February 2023:

You might imagine that nothing could prevent a Labour victory at the next election. The Conservatives could scarcely have done more to alienate voters and destroy public trust. Everyone knows that in this ridiculous first-past-the-post system, the only party in a position to replace them is Labour. Many will vote accordingly.
But there is one major obstacle: the Labour party. It seems determined to snatch defeat from the jaws of victory. How? By pursuing a civil lawsuit alleging breach of contract against five close associates of Jeremy Corbyn, whom it accuses of leaking a highly sensitive report.

The earliest occurrences of the phrase to snatch victory from the jaws of defeat and variants that I have found are as follows, in chronological order:

1-: From Collins’s Peerage of England; Genealogical, Biographical, and Historical (London: Printed for F. C. and J. Rivington, Otridge and Son, [&c.], 1812), by Egerton Brydges (1762-1837)—the following is about the British naval commander Horatio Nelson (1758-1805):

While every one of his victories may, for centuries probably, produce benefits of the most important kind, not only to the British empire, but to the whole civilized world, every one of them was gained under circumstances so singular and difficult, as nothing less than the powers of Nelson could have accomplished! It was Nelson’s sagacity that led his fleet a second time in pursuit of the French to the Nile; it was Nelson’s sagacity that gained a triumph, even in the jaws of defeat, over the Crown-Batteries of Copenhagen! it was Nelson’s sagacity that discovered the enemy’s destination, and saved our West-India Islands! It was Nelson’s sagacity, and daring courage, that by the genius of the plan, and the splendour of the execution, won the unequalled laurels of Trafalgar!

2-: From Letters from Gen. Winchester on the “History of the late War in the Western Country”, by James Winchester (1752-1826), published in the Daily National Intelligencer (Washington, District of Columbia, USA) of Saturday 26^th April 1823:

The glory attached to the memory of a brilliant achievement ought to be graduated by the responsibility assumed, and the obstacles encountered and overcome in its production; and no man is entitled to reap the iron harvest of military renown but him who has ploughed the field and sown the seeds of victory. General Jackson is entitled to more credit for his attack on the British army on the night of the 23d of December than for his subsequent defence of New Orleans on the 8^th of January: it was one of those masterly movements which, like that of Napoleon at Marengo, wrested the laurel of conquest from the very jaws of defeat.

3-: From the review of The Club-Book: Being Original Tales, &c. By Various Authors (London: Cochrane and Pickersgill, 1831)—review published in The Edinburgh Literary Journal; Or, Weekly Register of Criticism and Belles Lettres (Edinburgh, Midlothian, Scotland) of Saturday 6^th August 1831:

“The best laid schemes o’ mice an’ men gang aft ajee,” and it is curious to observe, how the lucky man will stumble on what is good despite of himself, even as Sir Frizzle Pumpkin encountered victory in the jaws of defeat.

4-: From the review of The Life of Lord Hill, G.C.B., late Commander of the Forces (London: John Murray, 1845), by the Rev. Edwin Sidney—review published in The North British Review (Edinburgh, Midlothian, Scotland) of August 1845:

All this, at least, should have been contained in any biography which was to do full justice to Lord Hill, and to show the British army with what intuitive promptness he could meet those sudden emergencies in which the indecision of a moment might have cost the loss of a battle, and with what varied resources both of prudence and daring he could bear up against apparently overwhelming dangers, until at length he compelled reluctant Fortune to his standard, and snatched a brilliant victory, as it were, out of the very jaws of defeat.

The earliest occurrences of the phrase to snatch defeat from the jaws of victory and variants that I have found are as follows, in chronological order:

1[?]-: From the explanations that General Winfield Scott (1786-1866) gave to explain the failure of the campaign he led in Florida during the Second Seminole War—as published in the Morning Courier and New-York Enquirer (New York City, New York, USA) of Wednesday 22^nd February 1837:

General Scott […] enters into the detail of the causes which, for 15 days after his arrival at Picolata, frustrated all his leading arrangements, and rendered it impossible for him to take the field […].
[…]
The intrusion of General Gaines, with a force destitute of supplies, and setting at nought all co-operation. By this, the supplies at Fort Drane, already insufficient for the intended movements, were consumed in an insulated attempt; the command of Gen. Clinch, and eventually that of Gen. Scott, compelled to abandon the movements for which their dispositions were made, and to occupy themselves in rescuing Gen. Gaines from the jaws of victory.

2-: From Local News, published in the Orleans Independent Standard (Barton, Vermont, USA) of Tuesday 10^th November 1868:

HOLLAND.

A Smart Thing.—An amusing affair occurred in Holland on election day. A few of the rebels who inhabit that town, and who of course shout themselves hoarse for Seymour and Blair, conceived the idea of electing that brace of worthies by strategy.—They knew (the foxy fellows) that if Holland could be carried for the rebs, Vermont was safe for Seymour, and if Vermont was secured the rebel ticket was, as a matter of course, certain of success, and Seymour would become president beyond a peradventure. The object was worth the trial and a few of them on election day left Derby Line very quietly and went to Holland, through the woods, calculating to surprise not only the stupid republicans, but the whole world by their sagacity. Like the swoop of so many eagles these buzzards appeared at the ballot box, deposited their ballots and breathlessly awaited the result, not once doubting that the “niggerhead-carpet-bagger-scallawag” party were disposed of not only for four years, but for all coming time, and that with the help of Jeff, Pemberton, Wade Hampton and Forrest, the country would be saved from the usurpations of a throne in the United States by U. S. Grant. Their anxiety was intense, the consequences were so momentous, but the time finally arrived for counting the votes. A careful count was made and resulted in a tie—one less than enough to produce another monster rebellion. Fancy their feelings! Defeat right in the jaws of victory! and after such pains too! As it is Vermont goes for Grant, and this with the other New England states, Pennsylvania, Ohio, and some fifteen or twenty more states, will very likely secure Grant’s election! What if Lee had called upon Derby Line for a larger quota wherewith to have invaded Holland! We tremble at the thought!

3-: From The Inter Ocean (Chicago, Illinois, USA) of Sunday 24^th May 1874:

BASE BALL.

The White Stockings yesterday earned their third defeat for the season. They were badly self-whipped, and in this lies their humiliation. Were they fairly defeated after having played a creditable game there would be no censure for them; but when they snatch defeat from the jaws of victory there can be little sympathy for their deserved misfortune. The spendthrift who throws away his earnings when he might command independence is entitled to less charity than the most impecunious but necessitous beggar.