It was a bright start to the game with both sides hitting the crossbar inside 25 minutes - Mark Noble first and Wahbi Khazri second - before Antonio gave the Hammers the lead on the half hour mark.
The Black Cats improved in the second period with Jermain Defoe having two great chances on his return to the club, but he couldn’t find the net.
There was a late flourish from both sides as the game drew to a close, with chances falling to Jack Rodwell and Andy Carroll, but Slaven Bilic's side held on for the three points to move up to fifth.
It was a bright start from both sides as both had equally great chances to take the lead four minutes apart.
The first came to the home side in the 19th minute when club legend Noble let rip from 25 yards after being teed up by Manuel Lanzini, but his first-time effort was brilliantly tipped onto the crossbar by Vito Mannone.
The second real chance of the game came from the mistake of Adrian after he was charged down, with the away side been given a free-kick moments later. From that, Khazri almost caught out the Spanish keeper but just hit the top of the bar.
Antonio strikes home
After that scare, the Hammers began to assert their dominance and managed to get the lead 30 minutes in. Antonio took advantage of Patrick van Aanholt's poor defending and beat the Dutchman on the inside before firing into the far corner.
He nearly had second seven minutes before the break too as he tried a spectacular volley from the edge of the area, but Mannone was equal to it as he pushed it around the post.
Allardyce's side came flying out of traps as the second period began and Defoe, on his return to the Boleyn Ground, had two great chances to get his current side back into the match.
The first came two minutes after the restart and it was the best of the two. Lee Cattermole's ball forward was misjudged by James Collins which allowed the striker to get through one-on-one, but he volleyed just wide of the post.
The second came two minutes later when Khazri managed to pick out the veteran striker, but his effort was just wide of the far corner - with his blushes been spared when the flag was wrongly raised for offside.
It was then the turn of van Aanholt in the 55th minute, who was looking to make up for his previous mistake, as he was set up by Khazri, but he hammered the ball over the crossbar from 12 yards.
The game died off after the Dutchman's wasted effort but, as the match entered the final 20 minutes, three great opportunities were carved out.
Substitute Rodwell was first up in the 74th minute as he wasted a golden opportunity to get the equaliser. DeAndre Yedlin was sent down the right and his cut-back was perfect for the midfielder, but Rodwell's shot from eight yards was straight at Adrian.
The home side came even closer four minutes later when Sam Byram headed Noble's cross back across goal for Carroll, but his volley from six yards clattered back off the crossbar.
Rodwell had the final real opportunity of the contest 12 minutes from the end when Khazri's low cross was poorly dealt with by Byram and his touch fell for the Sunderland man, but his effort was deflected over the bar in the last noteworthy action of the game.