Odemwingie was making his first start of the season after an ankle injury and the Nigerian striker had an eventful return.
He opened the scoring in the third minute after confusion in the Norwich defence but then went from hero to zero as his second half penalty was saved by young Norwich goalkeeper Declan Rudd.
That spot-kick miss couldn’t spark a Norwich fightback however and Roy Hodgson’s team held on to end a run of three successive defeats, while the Canaries are still waiting for their first victory after last season’s promotion from the Championship.
To complete a miserable day for Norwich, their striker James Vaughan was taken to hospital after an elbow from Gabriel Tamas left him with a serious facial injury.
Vaughan was flattened by Tamas at a corner in stoppage time in an incident, missed by referee Mark Halsey, which forced the forward to see a plastic surgeon to assess the extent of the damage.
Norwich manager Paul Lambert confirmed that Tamas’s stray elbow had left its mark on Vaughan’s mouth.
“James has gone to see the plastic surgeon at the minute, and it is a bad one. It has gone straight through the lip and they can’t just stitch it up, the specialist has got to look at it,” Lambert said.
“He had got a really nasty gash in his upper lip, which will need a bit of work on it.”
In the day’s other game, Blackburn remained rooted to the bottom of the table after Bobby Zamora’s equaliser gave Fulham a 1-1 draw at Craven Cottage.
Steve Kean’s struggling side had taken the lead through a fine strike from Ruben Rochina in the first half, but Zamora equalised soon after to leave Blackburn still waiting for their first league win this season.
There was more bad news for Kean as midfielder David Hoilett was stretchered off in stoppage time wearing a neck brace after a nasty collision with Fulham goalkeeper Mark Schwarzer.
Fulham are also without a victory in their first four league games and, like Blackburn, they were unable to climb out of the bottom three after a scrappy encounter in west London.
“He’s got three or four stitches in the side of his head and a bang on his eye,” Kean said of Hoilett’s injury.
“It’s not a great challenge and he’ll have some concussion. It’s a bad one.
“He was out for a little bit of time and it might affect him for the next game, but he’ll be fine.”