Nikica Jelavic put Everton ahead with a clever backheel before Jonny Howson equalised just prior to half-time with his first Norwich goal.
Jelavic added his fourth goal in four games to make it 2-1 in controversial circumstances after Norwich thought they should have had a free-kick, but the home crowd breathed a sigh of relief as Holt calmly swept home his 13th Premier League goal of the season with 14 minutes at Carrow Road to see the Canaries to the 40-point mark.
Holt, who was in and out of the Norwich starting XI early in the campaign, was a constant threat to a stubborn Everton defence throughout and remains the second-highest English goalscorer in the Premier League, behind only Wayne Rooney.
The draw means that Norwich have now reached the points tally commonly associated with safety with six matches left - a feat many would have thought impossible last summer when they were promoted after a six-year absence.
Everton, meanwhile, remain in seventh and boss David Moyes will be pleased to see Jelavic among the goals ahead of next week's mouth-watering FA Cup semi-final against Liverpool.
Everton, who were searching for their third straight win, started brightly.
Magaye Gueye picked out Jelavic at the back post but he failed to connect properly with his header.
The hulking frame of Holt was proving to be a nuisance for the visitors.
Jagielka brought down the striker on the edge of the box but Elliott Bennett drove straight into the wall from the resulting free-kick.
Norwich were struggling to get into the game and went behind in the 22nd minute.
Leighton Baines burst down the left and found Phil Jagielka, who crossed for Jelavic to flick home from close range.
Everton almost went 2-0 up moments later when Tony Hibbert's cross struck the woodwork but Tim Cahill failed to poke home the rebound.
Baines was booked for clambering over Elliott Bennett's back as the Canaries looked for an immediate response.
Wes Hoolahan and Andrew Surman were industrious in midfield but Everton's robust defence prevented them from fashioning any serious attempt on goal.
That was until the 39th minute, when Howson equalised.
Adam Drury released Hoolahan down the left flank and he cut inside and squared to the former Leeds man, who calmly slotted home from six yards.
Baines sent David Fox tumbling with a studs-up challenge soon after and the left-back was lucky to avoided a second yellow.
Norwich started the second half brightly. Marriner waved away appeals for a penalty after Surman's free-kick struck Pienaar, and Holt headed straight at Tim Howard.
The American then spilled Howson's fierce strike but Everton scrambled the ball clear before Holt could convert the rebound.
Norwich were starting to win the battle for supremacy in midfield and Moyes called on Marouane Fellaini, who replaced Phil Neville.
Norwich went behind again amid furious scenes on the hour. Pienaar went down under a challenge and held the ball between his legs. Norwich appealed for a foul, but Marriner's whistle never came. Fellaini then picked up the ball and found Baines, who laid off to Pienaar and his cross was converted by Jelavic from close range.
The Canaries players were incensed that the referee had not given a foul against Pienaar, who enjoyed the moment by celebrating in front of the home fans.
Holt unleashed a fierce free-kick that flew just over after a deflection, and Norwich were level after 76 minutes thanks to the Cumbrian's 15th of the season in all competitions.
Tim Howard spilled Aaron Wilbraham's shot straight back into the path of the Canaries forward and he held off the challenge of four Everton players to square to Holt, who calmly swept home.
Moyes brought on Victor Anichebe for Cahill with 10 minutes to go, but it was Norwich who looked the more likely team to grab a winner.
Elliott Bennett and Holt both went close in the dying minutes but Elliott Ward had to be at his strongest to deny Anichebe moments later.
Jelavic fell to the floor dramatically in injury time after clashing with Ryan Bennett. The striker went down clutching his jaw but replays showed the Norwich player had barely touched the Toffees marksman.
Andrew Crofts came on in the final seconds for Norwich but his introduction made no difference as the Canaries had to settle for a single, but hugely important, point.