It was the away side who started the better, and they so nearly took the lead after three minutes with an effort from Darron Gibson, but it drifted wide.
It might have been two moments later when Jelavic struck the post, but Tim Cahill somehow fired wide with the goal gaping.
Norwich continued to struggle for chances as the opening period progressed, with an Andrew Surman effort after 35 minutes their best of the half.
Everton regained the lead just past the hour mark with Jelavic's second, but a hint of controversy surrounded the strike with Pienaar seemingly holding the ball between his legs before finding the Croatian striker.
Norwich were level after 76 minutes, however, when Holt tapped home from close range after Aaron Wilbraham had tested Howard.
Marouane Fellaini came closest to winning it for Everton late on, but it wasn't to be, as the points were shared.
Everton remain in seventh in the Premier League table, while Norwich have moved into 11th.