GRANT Holt grabbed his sixth goal in eight Barclays Premier League games as the Canaries battled hard to earn a useful away point against Everton at Goodison Park.
Holt still had work to do when he picked up Morison's knock-down with his back to goal in the 28th minute, but he executed a superb drag-back to beat his man and find the net with a low shot off the far post for his seventh goal of the season.
City were also indebted to some excellent saves from John Ruddy, returning to his former club, and fine blocks from Russell Martin and Marc Tierney as Paul Lambert's side fought hard to keep Everton's attacks at bay.
In the end they were denied the victory when Leon Osman diverted substitute Royston Drenthe's strike into the net eight minutes from time to claim a share of the spoils for the Toffees.
A point away from home at Everton would have probably more than satisfied many of the Yellow Army before play and the fact that they ended up leaving Goodison slightly disappointed with that outcome signals the strides the players, staff and the Club have made together in recent seasons.
After the game Lambert told Canaries Player: "I thought we came here and performed really well and when you come here you know you're going to be right up against it and will have to defend for your lives sometimes because of the crowd they've got.
"Everton are a really good side, reagrdless of what anybody says they've got some really, really good players in there. But as a team I thought we stuck to our tasks and we got a really good goal to keep a foothold in the game.
"You've got to really weather the storm at times but defensively some of the tackles we've made and blocks we've made we're terrific and that's what the lads do for me week-in-week-out. It's a point away from home and that's a decent point."
City were unchanged from the previous weekend's encounter which had seen them run out 4-2 winners at Carrow Road over Newcastle United.
Meanwhile Everton saw the return of Leon Osman to their starting line-up after their 1-0 defeat at the Emirates last Saturday - Rodwell and Drenthe only making it back to the bench after injury.
In a slow opening to the game the first shot on goal came from City's Steve Morison on five minutes, a lay-off from Holt was met by the Welshman but his shot was too high to trouble Tim Howard.
Two minutes later it was Everton on the attack and former Evertonian John Ruddy did well to smother Marouane Fellaini's effort deep in the Canaries' box.
On nine minutes a burst of pace from Baines on the left saw him place a dangerous ball into the area, which forced Russell Martin into conceding a corner.
Martin was then forced to make a headed clearance from Osman's curling shot for another corner, which the Everton man took and saw his delivery flash across the face of goal.
The Toffees were having the better of the opportunities and on 19 minutes a ball was again dangerously placed into City's area after an Osman free-kick was initially charged down by the Canary wall.
Morison and Holt looked to combine four minutes later but the captain's ball back in was comfortably collected by Howard.
But on 28 minutes the combination did work when a Fox free-kick was headed down by Jagielka, Morison gathered and hooked the ball to his skipper, and with his back to goal and under pressure from John Heitinga, Holt managed to turn and find the far corner of the goal to put the visitors 1-0 up.
Saha went close on two occasions just after the half-hour with a deflected shot and then with a good effort on the turn which whistled just past the post.
On 39 minutes Hoolahan found himself in a great position after a good passing Canary move, but in the box instead of taking a shot himself he attempted to lift the ball to the back stick looking for Morison and Everton managed to clear their lines.
Two minutes before half-time and City won a free-kick far left which Surman whipped in and Morison managed to get a connection on it, but his header went wide of Howard's post.
Half-time: Everton 0, Norwich City 1
The opening of the second half began as the first, fairly even. The first opportunity came 10 minutes in when Osman tested Ruddy at his near post, the Norwich stopper forced to concede a corner kick.
Holt then went close on 58 minutes when he connected with a great diagnal cross into the area by Kyle Naughton, but it looped just over the upright to the disappointment of both Holt and the travelling Yellow Army.
David Moyes' made the first change of the game on 61 minutes with Denis Stracqualursi replacing Tim Cahill, which gave them an immediate lift, the foward nodding on for Saha to have a strike which Ruddy did well to block.
The Toffees were putting the Canaries under more pressure midway through the half with a succession of deep corners testing the City defence.
With 20 minutes left Everton went close again through Saha who just headed over Leighton Baine's left-wing cross.
Everton looked to add some pace to their attacks when Royston Drenthe replaced Gueye on 72 minutes and City responded when Paul Lambert brought on Bradley Johnson for Hoolahan.
The Canaries made another change with 10 minutes left - Steve Morison replaced by Aaron Wilbraham for his first Barclays Premier League appearance.
But a burst of pace from susbstitute Drenthe led to an Everton equaliser, his low shot was turned into the back of the net by Osman who stuck out his foot and steered it it past Ruddy to make it 1-1 with eight minutes left.
It gave the home side renewed confidence and Drenthe was proving a handful, and with four minutes left he let fly with a strong shot, which Ruddy did well to propel for a corner.
A final substitution from Everton saw Louis Saha come off for Conor McAleny and he too made an immediate impact almost getting on the end of a dangerous ball in the Canaries' penalty area, which had City hearts in their mouths, but they held on for a valuable and hard-worked Barclays Premier League point.
Final score: Everton 1, Norwich City 1
EVERTON: Howard, Hibbert, Baines, Heitinga, Jagielka, Saha (McAleny 88), Cahill (Stracqualursi 61), Neville (c), Gueye (Drenthe 72) Osman, Fellaini. Subs not used: Mucha, Bilyaletdinov, Distin, Rodwell.
CITY: Ruddy, Martin, Morison (Wilbraham 80), Whitbread, Crofts, Holt (c), Surman, Hoolahan (Johnson 74), Fox, Tierney, Naughton. Subs not used: Rudd, Jackson, Pilkington, Bennett, Barnett.