It was a poor first 45 minutes from both sides, with vague chances from Enner Valencia and Cheikhou Kouyate, with the first shot on target coming from Valencia five minutes from the break.
Eddie Howe's side started to get into the game in the second period, with chances from Adam Smith and Joshua King. The Hammers were given hope late on following the dismissal of Harry Arter, but the contest looked to heading for a draw until Antonio's header claimed all three points.
Slow start to the curtain-raiser
57,000 fans descended on Stratford ahead of the opening league game at the new home of the Hammers, with both sides looking to write the wrongs of their respective opening day results.
However the excitement in the stands, wasn't displayed on the pitch, as the first-half lacked any real chances or entertainment.
Antonio did well to get beyond Jordon Ibe in the 19th minute and get the ball to Valencia, but Steve Cook produced an excellent block to quell that attack.
Cook was at it again just before the half-hour mark, as Gokhan Tore did well to put the ball through to Kouyate, but the defender was there again to block.
The final 'opportunity' of the half was actually the first shot on target, as Valencia tested the palms of Artur Boruc, with the keeper doing well to get down to his near post and push the ball away.
Trying to get a bite of the cherry
Howe's side looked a different team as they get came out for the second period, and had two great opportunities to take the lead.
Adrian had yet to be tested, but got his first real test in the 49th minute when Smith cut down the right and unleashed a strike on goal, but it proved to be an easy save for the Spaniard.
He produced an even better save minutes later, as King tried one from 25 yards which the keeper did well to tip it over the crossbar,
Slaven Bilic's side went close to the lead just before the hour mark, Antonio did well to get the ball to the back post for Tore, but he could only clip it into the side-netting.
One man down
Bilic and his players were handed a golden opportunity to try and snatch the three points, as Bournemouth were reduced to ten men.
Arter was one of a handful of players that were booked in the first period, and late on, he brought down Kouyate who looked to spearhead a counter-attack, which left Craig Pawson with no option but to display the red card.
Snatching a win at the death
The majority of fans inside the London Stadium were urging their side on as the clocked ticked down, and with five minutes left, they took the lead.
After a barrage of chances, it was a simple finish to give them the three points, as Tore put a great ball into the back post and Antonio headed home for a historic moment in West Ham's history.