Rovers had been down to ten men for the whole of the second half and it should have been a formality after Mathias Svensson put the home side ahead 11 minutes after the break.
However, the visitors had other ideas and gave as good as they got, making City look second best for the last half-hour.
Dickov was a constant threat upfront and the Rovers defence stood firm against the Norwich forwards, making light of their numerical disadvantage.
The Canaries started strongly and in the fifth minute Darren Huckerby's corner was headed back by Craig Fleming and Svensson's header hit the bar and crept over.
It was nearly an unlucky 13th minute for Nils-Eric Johansson. He gave the ball away to Svensson who fed Mattias Jonson, but his effort drifted wide.
Leon McKenzie had two efforts blocked as City continued to dominate, before Brad Friedel denied Damien Francis ten minutes before the break.
Home keeper Robert Green was also in action before the break beating away two Jay Bothroyd piledrivers.
Two minutes before the interval the previously impressive Bothroyd blotted his copy book by kicking out at Jonson, leaving referee Steve Dunn no option but to produce a red card.
Green was tested by Tugay in the 48th minute, but from then on it was the visitors who did most of the attacking.
However, Norwich bucked the trend after 56 minutes when Svensson latched on to a knock down from Adam Drury's corner and hit a low, angled drive beyond Friedel to put the Canaries ahead.
Moments later Friedel was quickly off his line to cut out Huckerby's cross and then it was Rovers on the offensive again.
Fleming rescued City with a saving tackle after Dickov had got the better of Simon Charlton, before Johansson saw his powerful header rebound to safety off the crossbar nine minutes from full time.
Rovers were not to be denied however, and Dickov timed his run to get on the end of a right-wing cross from Lucas Neill, beating Green at the near post with a downward header to earn the visitors a deserved point.
Man of the Match: Paul Dickov - His constant probing at the heart of the City defence, especially after he had lost the support of Jay Bothroyd, was excellent. He rounded off a good away day for Rovers with a deserved equaliser.