All three Everton goals came against the run of play and in addition to their two goals the home side saw two goalbound efforts blocked on the line as Norwich were given a cruel lesson in finishing by the Premiership high-flyers.
Nigel Worthington's side kicked off attacking the River End goal and Leon McKenzie had a good chance to break the deadlock inside the first minute. Darren Huckerby floated a left-wing free-kick to the far post where his striking partner headed the ball into the ground and Nigel Martyn saved easily.
With Everton's first attack Leon Osman brought a save from Robert Green with a low shot.
The visitors survived a spell of pressure from the home side and took the lead in the tenth minute when Marcus Bent released Osman on the right. His low cross eluded everyone inside the six-yard box and was driven past Green by Kevin Kilbane with a firm right-foot shot at the far post.
This heralded a spell of pressure from Everton that penned Norwich back and the hosts had to deal with a string of crosses and long throws from Thomas Gravesen.
When the home side did break out Huckerby set up Damien Francis but his long-range effort sailed high over the bar.
Huckerby then fired high and wide from the left side of the Everton penalty area.
His cross from the left floated over Martyn but there was no Norwich player on hand to put it in the net.
When Everton hit back Bent's header was kept out by the back of Adam Drury's head.
Lee Carsley was booked in the 37th minute for a foul and then Norwich created their best chance of the first half when McKenzie crossed from the left, but Francis headed wide at the far post.
Having absorbed the Norwich pressure, Everton broke quickly and when Gravesen released Bent with a throughball down the inside right channel, the striker's low right-foot shot beat the advancing Green and rolled inside the far post.
The goal brought a chorus of: "We're going to win the league," from the away fans.
Thomas Helveg was replaced by Mathias Svensson at half time with Huckerby taking up a position on the left wing.
However, it was a break down the right which pulled a goal back for the Canaries.
Svensson released McKenzie who burst into the visitors' penalty area, shrugged off a challenge before drilling his left-foot shot between Martyn's legs from eight yards.
The Everton keeper was beaten again nine minutes later. McKenzie's shot was blocked by Alan Stubbs but, when Mattias Jonson headed Huckerby's left-wing corner back across the face of goal, Francis made up for his first-half miss, planting a firm right-foot shot past Martyn from close range.
On the hour Everton manager David Moyes made a double substitution replacing Osman and Tim Cahill with Steve Watson and Duncan Ferguson.
McKenzie did well on the right but his cross was cleared.
Green got down well to save Kilbane's low shot, while at the other end McKenzie was inches away from getting a foot on the end of Huckerby's inswinging left-wing cross.
The Norwich comeback was halted by Ferguson when he arrived at the far post to meet a right-wing cross from Watson which beat Green.
To their credit the Canaries did not give up and Huckerby set up McKenzie but he fired over.
Francis was unlucky not to score a deserved equaliser when his volley struck Carsley on the arm and was cleared.
Joseph Yobo came on for Bent in the 79th minute and four minutes later Worthington made a double substitution replacing McKenzie and Jonson with Gary Doherty and David Bentley.
Everton defended in depth and the nearest Norwich came to equalising was a shot from Svensson which flew inches the wrong side of the post.
Man of the Match: Marcus Bent - The Everton striker led the Toffees line on his own until the introduction of Duncan Ferguson on the hour and his goal was reward for a selfless display of frontrunning.