Bowen, touted for an England call-up by West Ham manager David Moyes, had one effort ruled out in the first half but was not to be denied as he headed home in the 42nd minute.
"It was a good performance. Norwich are fighting for points. We had to put the barricades up a little bit but with our attacking threat we've always got a goal in us," Bowen said.
"We hit a bit of a rough patch and we were disappointed with our performances but that shows the standards we have set ourselves. We'll just keep going about our business."
Bowen has been directly involved in 12 Premier League goals this season with five goals and seven assists.
And his form is helping West Ham maintain their push to try and bring Champions League football to the London Stadium.
"His all-round play is improving. He has been great for us and has got goals and assists in him," Moyes said.
Bowen could have had a hat-trick had his first-half effort not been ruled out because Nikola Vlasic was adjudged to have been in an offside position and interfering with Krul.
Norwich, who have now lost six league games in a row without scoring, competed well in the first half but slipped behind when Bowen nodded in Vladimir Coufal's cross.
Bowen also struck the woodwork twice but Norwich were close to a surprise leveller when Idah showed great footwork before firing a shot that Fabianski touched against the post.
Bowen then sealed the points to send the West Ham fans home happy and leave Norwich sinking fast.