Watkins then thought he had made amends in stoppage time, but he had a goal ruled out by VAR for a marginal offside.
Jack Grealish had levelled with a deflected effort in the 25th minute, but it was a frustrating night for Villa who could have gone fourth with a win.
West Ham's third successive victory leaves them on 17 points from 10 games, four points behind leaders Tottenham Hotspur. Villa have slipped to 10th with 15 points, having played a game less.
Three weeks ago West Ham beat Fulham 1-0 at the London Stadium after a comical last-gasp penalty miss by Ademola Lookman and they got lucky again as they bagged the points, despite being second-best for much of the game.
"We've missed a penalty and had a goal disallowed for a part of his body that can't actually be used to put the ball in the net anyway," Villa manager Dean Smith said.
"The goal Ollie scores they've given offside for his arm, but the only reason his arm is there is because he's being fouled. It's either he scores or it's a penalty."
Villa were caught cold as Ogbonna rose unchallenged to head West Ham into the lead after two minutes.
But they responded well and Grealish exploited a hole in the middle of West Ham's defence to burst forward and strike a shot that deflected past Lukasz Fabianski.
West Ham manager David Moyes sent on Said Benrahma for the second half and almost immediately he set up Bowen to head his side back into the lead.
The hosts never looked comfortable though and Villa should have levelled when Grealish released Watkins and he pulled the ball back for Trezeguet who somehow failed to beat Fabianski from point-blank range.
Villa were awarded a penalty, via VAR, when Declan Rice was adjudged to have pulled Trezeguet's shirt, but Watkins leant back and sent his spot kick against the bar.
Watkins should have had the last laugh but after breaking free of Ogbonna, who had his arms around the striker's neck, to slot in from a low cross his joy was cut short because, according to VAR, part of his arm was offside.
Moyes was not complaining and pointed to Rice being hard done by for the Villa penalty.
"I'd like referees to toughen up a bit and not give every decision," he said.