Starting on reversed-grid pole after a troubled race on Saturday, Bird made a fine start and was never challenged at the head of the field.
The only aspect he failed to achieve, however, was the two extra points for fastest lap, but fortunately for him Leimer also failed in his efforts to get it.
It was Bird's fifth win of the season, and he closes to within seven points of Leimer.
Marcus Ericsson finished second for DAMS, ahead of Leimer (Racing Engineering) and Stephane Richelmi in the second DAMS machine.
A bizarre incident then befell Leimer on the slowing down lap, when he slammed into Alexander Rossi's Caterham car.
Rossi was making the sharp-left turn off the track to enter the support-race paddock, as Leimer was cruising to complete the lap to the podium. Leimer appeared to have injured his left wrist slightly.
Jon Lancaster rose from ninth to fifth, but was mainly a beneficiary of drivers ahead of him struggling on used rubber or the super-soft option tyre, which could not last anywhere near the 20-lap race stint required.
That included Saturday's race-winner Jolyon Palmer, who finished 17th after a pitstop.
It promoted unlikely points finishers Johnny Cecotto Jr, Daniel de Jong and Adrian Quaife-Hobbs, who all started from well down the grid.