The powerhouse striker stabbed the ball home from close range in the ninth minute after Burnley defender James Tarkowski failed to clear a cross, Antonio's 40th Premier League goal for the club.
In line with COVID-19 guidelines Antonio opted for a solo celebration of his 40th Premier League goal for the club -- laying on his back and motioning as if swimming backstroke.
"I had a game of Call of Duty with Declan [Rice] and lost and that was the forfeit," Antonio said.
West Ham have 29 points from 18 games while Burnley, who have yet to reach double figures in goals scored this season, are looking anxiously over their shoulders in 17th place.
Only Paolo Di Canio (47), Mark Noble (46) and Carlton Cole (41) have reached the 40-goal mark in the Premier League for West Ham and Antonio deserves his place on that list.
Strong and powerful he was a constant thorn in Burnley's side as he returned to the starting lineup in the league after some substitute appearances following a hamstring injury.
He could not believe his luck though for his goal. Tarkowski looked favourite to head away a cross from the left by Pablo Fornals but he made no contact and the ball arrived to Antonio who finished from close-range past Nick Pope.
Burnley offered little before the break and could have fallen further behind when Ogbonna hit the post from the lively Bowen's cross. Bowen had a glorious chance after the break and Rice curled a free kick over.
Sean Dyche's side showed more purpose in the latter stages but never really looked like scoring as West Ham recorded a fourth successive clean sheet in all competitions.
"Not our best performance but another resilient one," manager David Moyes said.
Burnley have managed only five shots on target in their last three Premier League games and urgently need to start scoring if they are not to be dragged into a relegation dogfight.
"We had a lot of possession but couldn't quite open the door and that's been our problem all season," Dyche said.