Michail Antonio, who scored all the goals in a 4-0 rout last time the Hammers visited Norwich at the end of the 2020 season, had made it 2-0 on the half hour with his first league goal since Jan. 1.
The first three goals were all assisted by Bowen.
The Canaries thought they had pulled one back in the 47th when former West Ham defender Sam Byram netted but a VAR review ruled it out for handball.
Manuel Lanzini made it 4-0 from the penalty spot in the 65th after another VAR review found Danish midfielder Jacob Soerensen had handled.
Victory left the Londoners on 55 points and three behind Manchester United, who lost 4-0 at Brighton on Saturday and have played one game more.
David Moyes's side lost their Europa League semifinal to Bundesliga side Eintracht Frankfurt 3-1 on aggregate on Thursday but found the perfect remedy for that disappointment in bottom-ranked opponents who were booed off at halftime.
Norwich have now lost 12 home league matches this season.