Grant Holt and Doherty were on target to deny the Seagulls their first home league win under boss Gus Poyet.
Former Wolves winger Elliott Bennett gave Brighton a 21st minute lead with a low free-kick through a crowded area.
Leading scorer Holt, returning from suspension, levelled with his 24th goal of the season 10 minutes from time with a deflected shot into the roof of the net.
The Canaries snatched maximum points in dramatic fashion as defender Doherty got up to head in a free-kick from Darel Russell on 84 minutes.
Norwich, now four points clear at the top of the table, were indebted to goal line clearances by Michael Nelson and Simon Lappin from efforts by Glenn Murray when they were a goal behind.