Both teams started the game well but it was the Toffees who had the better of the opening exchanges, most notably Nikica Jelavic who repeatedly found space in the box. The Croatian's best chance came as he controlled the ball brilliantly before firing goalwards but Mark Bunn was equal to his effort getting down well to parry away.
Norwich did show signs of invention but it always seemed as if it was only matter of time before Everton took the lead and they finally got their reward on 39 minutes, as Leighton Baines picked out Leon Osman with a cross and the midfielder stooped low to head home.
The Merseysiders continued to push after the break but everything changed when Kei Kamara was introduced on the hour mark.
The Sierra Leone striker made a huge difference, adding massive impetus to the Canaries' attack, forcing a great save from Tim Howard after 63 minutes before headering just wide moments later.
However, he finally got his reward after 84 minutes, rising above Marouane Fellaini at a corner and heading down and into the goal to send the Canaries into rapture.
The home side continued to push on after that score and after Grant Holt went close on 90 minutes, the skipper grabbed a dramatic winner, latching onto Russell Martin's deep cross to poke home at the back post to grab a vital three points.