The £2million summer signing stepped in for leading scorer James Beattie, who has been linked with a £3million move to Premier League side Stoke.
The former Watford hitman struck in the 17th minute as the Bramall Lane side struggled to finish the job against a Norwich team flirting with the drop zone.
United made a promising start as Stephen Quinn tested David Marshall with a low shot which was smothered on the line by the Norwich keeper, before lashing in a left-foot strike which saw the ball crashing against the bar.
United broke the deadlock with a textbook goal. Henderson sparked the move by playing the ball wide to Danny Webber on the left flank.
He produced an inch-perfect cross to Henderson who was waiting at the far post to finish in clinical fashion with a firm header past the helpless Marshall for his third of the season.
The former Watford targetman almost grabbed a second but his 25-yard strike was scooped up by the diving Norwich keeper.
Struggling Norwich, with just one win from their last six games, almost found a way through with Antione Sibierski picking out Arturo Lupoli, but Paddy Kenny snatched the ball away.
United escaped three minutes before the break when they failed to cut out Mark Fotheringham's cross from the right.
Wes Hoolahan's downward header from six yards smacked against the bar before Kenny foiled Lupoli by spreading himself to block his fierce strike.
Marshall pulled off a spectacular double save from Henderson as he palmed away his right-foot strike from a Billy Sharp cross and when the striker lashed in the loose ball, the Norwich keeper foiled him again.