The Hammers, who had lost their four previous matches against Wolves without scoring, went 1-0 up on 17 minutes. A quick free-kick from Pablo Fornals picked out Bowen, who expertly curled a low shot beyond Rui Patricio.
Fornals blasted over from close range in an opening 45 minutes dominated by the home side.
West Ham doubled their tally in the 57th minute when Bowen tapped in a loose ball after Fornals' long-range effort hit the post.
The Hammers added a third when Tomas Soucek's header from Aaron Cresswell's corner was deflected in for an own goal by Raul Jimenez.
Sebastien Haller headed in a fourth in stoppage time, meaning West Ham and Wolves now both have one victory from their opening three matches.
Budweiser King of the Match: Jarrod Bowen
West Ham: 4 Oct v Leicester (A)
Wolves: 4 Oct v Fulham (H)