Cureton had been booed for the entire match by U's fans who had been disappointed with the way he left the club last summer, having stated that Colchester 'lacked ambition'.
But the 32-year-old had the last laugh when he forced Colchester left-back Danny Granville to score an own goal with just 90 seconds remaining.
Defender Gary Doherty nodded down Lee Croft's free-kick into the six-yard box, where Granville could only divert the ball home with Cureton waiting to pounce behind him.
Just ten minutes earlier, the U's had taken the lead in what had been a very scrappy game.
It was a also a scrappy goal, with Norwich left-back Mo Camara allowing Johnnie Jackson's corner to sneak past him at the near post, enabling Kevin McLeod to steer home a loose ball into the roof of the net from point-blank range.
McLeod's goal looked to have been enough to record what would have been only Colchester's second victory in 11 games, but the visitors rallied strongly in the dying minutes.
There were appeals for a penalty turned down when substitute Croft appeared to have been fouled in the box, and then midfielder Darel Russell was denied an equaliser by the woodwork.
Russell's header from substitute Darren Huckerby's cross struck the inside of the far post and rolled to safety.
But Colchester could not hang on and so therefore remain in the relegation zone. They have collected just seven points from a possible 33 in their last 11 games.
Norwich boss Glenn Roeder admitted after the draw: "The way the game panned out, I think this was a point gained rather than two lost.
"We didn't play well, but what you can say about this set of players is that they never give up."
Colchester boss Geraint Williams rued: "This time we got to within 90 seconds of getting the win. We've got to learn to be professional and close out these games."