After a night of close calls at both ends, the Canaries captain had the easiest of tasks in the 89th minute when the ball fell to him a few yards from goal, after Hoops keeper Fraser Forster had blocked a drive from Jonathan Howson, to slam the ball into the net.
Celtic manager Neil Lennon was in Iceland to see KR Reykjavik play HJK Helsinki in the Champions League qualifiers, with the Finnish side winning 2-1 on Tuesday night for a 9-1 aggregate success which sets up a trip to Parkhead next week in the first leg of the third qualifying round.
Lennon will already know following Saturday's 4-0 friendly defeat by Ajax in Amsterdam, that his side will have to improve if they are to get into the Champions League play-offs.
Norwich boss Chris Hughton named a team for the first half, including former Rangers defender Steven Whittaker, and a team for the second half.
Whittaker was jeered when touched the ball and when he went off injured in the 21st minute, to be replaced by Russell Martin.
Before and after that, both sides had chances to break the deadlock but it was a first half of near misses.
City had efforts from James Vaughan and Anthony Pilkington before a far from full strength Celtic side came close to opening the scoring through Kris Commons.
The midfielder's deflected shot in the 22nd minute hit the top of the bar and then, after Norwich had survived the corner, his cross into the box was headed on to the bar and over by right-back Mikael Lustig.
Hoops goalkeeper Lukasz Zaluska produced a fine block at his near post from Anthony Pilkington before City keeper John Ruddy made a decent save from Filip Twardzik's 25-yard drive down at his right-hand post at the expense of a corner which came to nothing.
Celtic captain Georgios Samaras then passed up on a decent chance when he was set up by Dylan McGeouch.
Having lost defender Kelvin Wilson to injury already, the home side lost their keeper two minutes from the break.
A clash between James Vaughan and Zaluska left the Pole requiring treatment before he was replaced by Forster.
Commons went close with a drive from distance seven minutes after the break before Forster stuck out a foot to block Chris Martin's close-range flick at the other end.
Moments later Samaras missed a great chance when he was sent clear by Paddy McCourt but the Hoops forward lobbed the ball high over the bar with Ruddy in no man's land.
With four minutes remaining Forster was almost caught out by Simeon Jackson's long-distance drive but the keeper had less luck when Holt, one of the second-half substitutes, pounced moments later.