NORWICH punished Everton for their first half profligacy by fighting back to earn a 1-1 draw at Carrow Road.
Romelu Lukaku headed the Toffees into a first half lead but should have scored two more as City struggled to combat their fluidity in attack, with Leighton Baines also striking the post.
The second half was a different story, however, after Wes Hoolahan bundled in a leveller for the Canaries less than two minutes after the restart.
Cameron Jerome should have scored the winner, but Alex Neil will draw plenty of encouragement from another swashbuckling second half performance on home turf.
Their 2-0 defeat to Watford last weekend led to Alex Neil making four changes for this game as Hoolahan returned from his knee injury.
Also taking their place in the starting eleven were captain Russell Martin, Gary O'Neil and Jerome - Ryan Bennett, Graham Dorrans, Jonny Howson and Lewis Grabban dropped to the bench.
Everton welcomed back Baines for his first start of the campaign, with Brendan Galloway having to settle for a place among the substitutes. Gareth Barry captained the Toffees in Phil Jagielka's continued absence.
Neil had hinted at a more expansive approach in the build-up to the game and City certainly didn't hesitate in closing their opponents down sharply in the opening exchanges.
Nathan Redmond and Alex Tettey both saw half chances fly over the bar, before in-form Lukaku hit a first-time shot wide when Andre Wisdom's clearance was blocked into his path.
Three minutes later, however, Everton's star striker extended his rich vein of goalscoring form by bagging the opener.
City failed to clear their lines through Martin Olsson and Gerard Deulofeu was able to pick out Lukaku at the back post, and he nodded the ball back across Declan Rudd into the net.
The visitors were denied a second four minutes later when Rudd was called into action to deny Arouna Kone, who had been played clean through on goal by Lukaku.
Neil's team responded by continuing to try and play their football but the next opportunity fell to Everton and Lukaku, with the striker guilty of missing a simple chance at the back post when Tom Cleverley's cross deflected off Martin into his path.
Everton should have been out of sight with the chances they created, with Baines next to go close when he rocketed a half volley off the inside of the post from Seamus Coleman's delivery.
Rudd blocked Kone again before Lukaku dragged an effort wide, and after the Belgium international saw another shot fly narrowly past the post in stoppage time, City will have been relieved to hear the half-time whistle.
HALF-TIME: Norwich City 0-1 Everton
Neil brought on Bennett at half-time in place of Wisdom, a move that saw Martin move to right-back.
Then just a minute-and-a-half into the second period, City were level. Bennett made an immediate impact in Everton's box, winning Robbie Brady's corner in the air.
Hoolahan was there, bundling the ball in on the line despite the best efforts of John Stones to keep it out.
City were rejuvenated and suddenly the game was turned on its head - they could have edged ahead when Jerome closed in on Brady's corner, but Hoolahan got in the striker's way and Everton cleared.
Martinez's side still carried a significant threat on the counter-attack, but it was the Canaries who dictated the game's tempo, forcing their opponents into a change when Deulofeu was replaced by Kevin Mirallas.
With 20 minutes left on the clock, City created a golden opportunity to go ahead - Martin broke into the area and Hoolahan backheeled the ball to Jerome, but the frontman somehow shot over from six yards.
Rudd hadn't been kept as busy after the break, but he made another superb stop to deny Barry when he was found by Kone.
Everton didn't carry the potency they did in the first half, however, and when the final whistle blew, City deserved their point.
FULL-TIME: Norwich City 1-1 Everton
GOALS: Canaries: Wes Hoolahan (47) - Toffees: Romelu Lukaku (15)
NORWICH CITY: Rudd; Wisdom (Bennett 45), Martin (c), Bassong, Olsson; Redmond, O'Neil, Tettey, Brady; Hoolahan (Howson 84); Jerome. Subs not used: Ruddy (GK), Grabban, Mbokani, Dorrans, Mulumbu.
EVERTON: Howard; Coleman, Stones, Funes Mori, Baines; Cleverley, Barry (c); Deulofeu (Mirallas 69), Barkley (Gibson 76), Kone; Lukaku. Subs not used: Robles (GK), Lennon, Naismith, Osman, Galloway.
REFEREE: Martin Atkinson
GOLDEN GOAL TIMES: 14:47, 46:04