A Gary Doherty own goal maintained Everton's push for Europe but saw Norwich leave another away ground empty-handed despite a brave display.
The Canaries defender put through his own net under pressure from Duncan Ferguson after Robert Green had superbly saved Marcus Bent's header.
Green earlier produced excellent stops from a Lee Carsley free-kick and a deflected Kevin Kilbane shot.
Darren Huckerby and Dean Ashton failed to convert Norwich's best chances.
But the visitors seemed unlucky not earn a penalty as Alan Stubbs appeared to handle the ball in the penalty area late on.
It was a bit of late drama for a game that had started in poor fashion.
Everton had recalled fit-again goalkeeper Nigel Martyn in place of Richard Wright.
But Martyn had so little to do during the first half, he could have played even if he had not recovered from the calf injury which kept him out for six matches.
Huckerby was lively up front for Norwich, who were still seeking their first away victory of the season.
But given the lacklustre nature of Huckerby's finishing, along with strike partner Ashton, three points on the road did not look likely.
A screwed shot wide from Huckerby and a tame effort from Ashton were the best the Canaries could manage in the opening half.
Everton fared even worse, in their best chance Tim Cahill demonstrated how to tie yourself in knots when attempting to volley Carsley's nodded pass.
Even Toffees' boss David Moyes got in on the act, falling flat on his back when trying to control the ball which came his way in the technical area.
It raised a smile from opposite number Nigel Worthington, and was probably the most entertaining moment of the first half.
Everton took the chance to parade new signing Mikel Arteta during the interval - and how they could have done with him fit and available.
Graham Stuart was handed his debut after signing for Norwich on loan, as he replaced the injured Adam Drury at half time.
The hosts were first to threaten after the interval, when Green was at full stretch to save Kilbane's deflected shot.
And just after he watched nervously as Beattie's dipping shot cleared the bar.
As the game suddenly opened up, Huckerby found himself behind the Everton defence, but once more was off target with his effort.
With space to be exploited, Everton brought on Ferguson for defender David Weir just after the hour.
But it was Carsley who almost broke the stalemate, when he aimed a curling free-kick at the top corner.
It took a smart save from the increasingly busy Green to prevent a goal.
However, Everton's push for an opener left them exposed at the back and an unmarked Ashton should have directed his header away from Martyn.
And seconds later, Martyn was again called into action as he saved well from Huckerby's shot.
Kilbane was next to try his luck as Ferguson's presence caused problems in the Norwich defence, but he headed wide.
But with Norwich struggling to cope with Ferguson's physical style, it was no surprise when the Scot was involved in Everton's winner.
Fellow substitute Bent forced an excellent save from Green, but Ferguson pressured Doherty into turning the rebound into his own net.
The win leaves Everton still on course in their push for a Champions League spot, only four points behind third-placed Arsenal.
Everton assistant boss Alan Irvine:
"We are absolutely delighted. It would be nice to win by two or three goals but you get the same number of points for winning 1-0.
"Norwich made it very difficult for us and we expected that. It was hard work but I think we deserved it at the end.
"Norwich will probably go away feeling little but unfortunate, but we are very pleased with the result."
Norwich boss Nigel Worthington:
"I thought it was a magnificent performance. We stood up, passed the ball well, created chances and I feel disappointed for the lads.
"They played so well and worked so hard, but they have got nothing out of the game. It's disappointing.
"If we keep performing and working like that, Lady Luck may shine on us."
Everton: Martyn, Hibbert, Stubbs, Weir (Ferguson 64), Pistone, Yobo, McFadden (Naysmith 87), Carsley, Cahill, Kilbane, Beattie (Bent 76).
Subs Not Used: Wright, Chadwick. Booked: Hibbert.
Goals: Ferguson 78.
Norwich: Green, Edworthy, Doherty, Fleming, Drury (Stuart 45), Jonson (McKenzie 81), Holt, Francis, Brennan, Huckerby, Ashton.
Subs Not Used: Gallacher, McVeigh, Shackell.
Ref: A Wiley (Staffordshire).