Victory would have taken Everton to within a point of fifth-place Tottenham Hotspur, but after Romelu Lukaku gave them a 15th-minute lead, they squandered a glut of opportunities to extend their advantage.
Hoolahan duly levelled the scores early in the second half, scuffing in from close range to consign Everton to a third consecutive draw and inch Norwich a point clear of the relegation places.
Alex Neil's side might have emerged with all three points, only for Cameron Jerome to produce a glaring miss with 20 minutes remaining, hoisting the ball over the bar from Hoolahan's flick.
Gerard Deulofeu signalled Everton's ambition with an early driving run into the Norwich box and after Lukaku had dragged a shot wide, the Belgium striker put the visitors ahead.
Norwich left-back Martin Olsson's panicky clearance went straight to Deulofeu and the former Barcelona winger arced a beautiful cross to the back post, where Lukaku charged in to head home.
It was Lukaku's 15th goal of the season, in all competitions, and made him the first Everton player since Bob Latchford in 1975 to score in seven consecutive games.
With Norwich's defence all at sea, a second Everton goal seemed a matter of time.
Declan Rudd rushed out to save from Arouna Kone, before Lukaku somehow failed to turn the ball into an open goal from Tom Cleverley's right-wing cross.
Lukaku also shot narrowly wide twice, while England left-back Leighton Baines, making his first start of the season after a long-term ankle injury, slammed a right-foot shot against the post.
But Martinez's side - who eliminated Norwich from the League Cup in October - failed to make their dominance count and within seconds of the kick-off in the second half, they were punished.
Ryan Bennett, sent on for Andre Wisdom at half-time, met Robbie Brady's corner with a header and although Tim Howard parried, Hoolahan was on hand to bundle the ball over the line from close range.
The chances dried up momentarily, Ramiro Funes Mori blocking from Brady at one end, Olsson from Kone at the other, before Jerome wasted a gilt-edged chance to give Norwich victory.
Hoolahan's clever back-heel presented him with a clear sight of goal, but with the net at his mercy, the former Stoke City striker shanked the ball into the stands from six yards out. – AFP
Original source: Everton frustrated by Norwich