Ten man Brentford fell behind when Paul Caddis netted the spot kick after Tony Craig was sent off for bringing down former Bee Clayton Donaldson in the area early on.
But Odubajo, dropped for the starting line up for the first time in the league this season, came off the bench to score a stunning equaliser, storming don the right at pace before dinking the ball over the visiting keeper for his first goal in Brentford colours.
Bees boss Mark Warburton said: "I’m delighted though as the boys showed tremendous character and application there to come back. At half-time we re-grouped and I thought we played very well second half. We showed our quality on the ball, and by the end of the game there was only one team in it.”