After commanding much of the game Everton found themselves a goal down at Carrow Road through an unlikely Steven Whittaker goal early in the second half.
Two goals in four minutes just after the hour - the first a stunning effort from Ross Barkley before Seamus Coleman converted a tap-in - looked like putting Roberto Martinez on course for a win in his first game in charge of the Toffees.
But Norwich's club-record signing Van Wolfswinkel produced a fantastic header with a little under 20 minutes remaining to earn his new side a point.
The majority of the first half was dominated by Everton as Martinez stuck to the tried and tested Everton formation and familiar players with none of his summer signings starting in Norfolk.
The visitors only had a tame header from captain Phil Jagielka to show for their dominance in possession in the early exchanges before Whittaker lost the ball after needlessly dawdling inside his own penalty area, but Steven Pienaar could not capitalise and bent his shot over the crossbar.
The home side finally came to life after 15 minutes when Bradley Johnson's pass was knocked into the path of Elliott Bennett by Wes Hoolahan, but ?8.5million summer signing Van Wolfswinkel's header was deflected behind for a corner.
Van Wolfswinkel was involved again moments later as he latched on to a fine long ball by Russell Martin and crossed towards Hoolahan, only for Sylvain Distin to make a diving clearance in front of the Republic of Ireland international.
That period of domination for Norwich seemed to stir Everton and they again took control of proceedings with Kevin Mirallas firing just wide of John Ruddy's right-hand post after a neat interchange with Nikica Jelavic.
Mirallas again came close to opening the scoring just before the half-hour mark as his effort from Coleman's cross was defected behind off Martin. The Toffees started to dictate the tempo as the first half drew to a close but they still could not truly test their former goalkeeper Ruddy.
Source: PA
Source: PA