Aided by the phonetic similarity between the two nouns that it contains, the phrase in the grip of the grape means under the influence of alcohol.

This phrase has, in the course of time, been coined on separate occasions by various persons, independently from one another.

In fact, an isolated occurrence of in the grip of the grape, the earliest that I have found, does not refer to alcohol, but to grapefruit; it is from The Bystander (London, England) of Wednesday 4^th May 1921:

In the Grip of the Grape
Everybody seems to be eating grape-fruit. At breakfast one comes down to a neatly cut sphere of fruit which your hostess tells you will double your appetite and halve your handicap. At lunch, at dinner, it is the same, only at the latter meal perhaps there is a suspicion of alcohol marring (?) the “grape’s” juice. Apparently the habit has come over with many other American domestic introductions, for there it is eaten continually—almost as much as “gum”—doctors recommending it as a panacea for all ills, especially colds and influenza. The Cuban “grape” is supposed to be best, for it can be eaten without the assistance of any sugar, and Americans contend that it has more “pep” in it. Certainly it is larger and cheaper than other varieties, and by interpreting “tonic” for “pep” they are probably not far wrong.

These are the earliest occurrences that I have found of in the grip of the grape used with reference to alcohol, in chronological order:

1-: From a letter that one Dr. N. Archibald Pitfall sent to the U.S. baseball player Cletus Elwood ‘Boots’ Poffenberger (1915-1999)—letter quoted by Fred Russell in his column Sideline Sidelights, published in the Nashville Banner (Nashville, Tennessee) of Thursday 14^th August 1941:

“No doubt you have heard of me, and of my great work on the lecture platform, in the cause of temperance. Perhaps you are familiar with some of my better known addresses, such as—‘The Sin of Gin,’ ‘In the Grip of the Grape’ and ‘Rum, Rye and Ruin.’

2-: From Request of Able-Seaman W. T. Door, a short story by William Marshall, published in The Australasian (Melbourne, Victoria) of Saturday 22^nd December 1945:

Jessie searched under the couch, and I was delighted to see her produce another full bottle of “bombo,” as I was badly in need of a drink. Some time later I began to feel rather queer, and beads of perspiration commenced to form on my forehead. Jessie noticed my distress and said: “You’re in the grip of the grape, pal; you’re [sic] eyes are going glassy, so get your head down and take it easy for a while.” Thankfully I laid down on the couch, and must have fallen asleep immediately.

Illustration for Request of Able-Seaman W. T. Door—The Australasian (Melbourne, Victoria)—22^nd December 1945:

—Miss O’Brien happened to be drinking a glass of port—or “bombo,” as she called it—

3-: From Lennie Looks at Omar Khayyam *, by Howard Trotter, published in The News (Adelaide, South Australia) of Saturday 18^th January 1947:

Lennie Lettitbee, squatting on the edge of the couch, wiggled his bare toes, flicked his braces against his chest, took a tug at his glass of port, and looked at his friend Sammy Soewatt over the edge of a volume of Omar Khayyam.
“Listen to what the priceless old Persian had to say about wine,” Lennie said between tugs. “‘I often wonder what the vintner buys, one half so precious as the goods he sells.’ The old wog knew what he was talking about.”
Sammy shuddered as he took a sip of his friend’s special reserve vintage. “Must have been in the grip of the grape,” he replied.
“Grip of the grape nothing,” Lennie retorted. “You’re like a lot of other Australians. Your palate’s so coarse that to pour wine over it is like smearing eau de cologne on a pig’s back.”

(* Omar Khayyam (1048-1131) was a Persian mathematician, astronomer and poet.)

4-: From the memoirs of the Australian boxer Billy Grime (1902-1952), published in the Evening Advocate (Innisfail, Queensland) of Wednesday 24^th November 1948:

The food I got at the private house where we stayed was terrible. I found out that the woman of the house was in the grip of the grape.
She spent our board money on booze instead of on food.

5-: From Dramas of the Courts, published in the Daily Telegraph (Sydney, New South Wales) of Sunday 5^th December 1948:

Charlotte Sarah Spray sank into the grip of the grape while her husband was away at the war.
And so heavy were her benders that she would pawn the household goods.

6-: From The Sun (Baltimore, Maryland) of Saturday 19^th May 1951:

The Grip Of The Grape

Arrested for abnormal staggering at Barclay street and Pitman place, Charles C. Bratt yesterday blamed all his troubles on illness.
Charged with being drunk on the street, the 40-year-old Negro admitted he had been in his cups.
But, he explained, he had to take medicine for his ailments. Before his arrest, for example, he’d taken four phenobarbital capsules, and, of course, washed them down with a little wine.
Then, he explained, he had downed a little more wine, strictly for its medicinal value.
Magistrate Marshall A. Levin, who takes his alibis with a grain of salt, fined Bratt $10 and costs.

7-: From the column Contact, by the Australian journalist Jim Macdougall (1903-1995), published in The Sun (Sydney, New South Wales) of Friday 14^th March 1952:

Alcoholism is a dreadful disease. Nobody knows its tragedy and perils better than the alcoholic.
He IS the victim: the helpless ship in a devouring gale.
Alcoholics Anonymous is the haven, but so few reach it.
A red-nosed character in the grip of the grape went along to an AA meeting in the Western Suburbs the other night, but it wasn’t what he expected.
He thought Alcoholics Anonymous was a place where you could drink in secret!