Bird was first across the line but the celebrations were muted, with the Virgin Racing driver aware that stewards were investigating a penultimate-lap collision with DS Techeetah's Andre Lotterer.
The impact at Turn Two punctured the German's right rear tyre and dumped the leader, a three-times Le Mans 24 Hours winner, out of the race.
The stewards imposed a five-second penalty on Bird, pending appeal, for causing a collision -- a sanction that promoted Venturi's Swiss driver Mortara into the top spot as the fifth different winner in five races this season.
Brazilian Lucas Di Grassi moved up to second place for Audi Abt, with Bird's Dutch team mate Robin Frijns third.
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Bird dropped to sixth but still regained the championship lead, one point clear of previous series leader Jerome d'Ambrosio who failed to finish for Mahindra.
The outcome was little consolation for Lotterer, who accused Bird of a "disgusting move".
"I lost it thanks to him. Even if you give him a penalty my race is done -- it's just sad," he said.
Lotterer had led from the eighth lap with Bird close behind but unable to get past on a narrow track in slippery conditions after earlier showers, with the race stopped early on and featuring three safety car periods.
"It's a shame," Bird said of the incident. "I tried to go down the inside and Andre late-defended. It's very slippery down the inside, I braked, locked up and hit him a little bit like what he did with JEV (Jean-Eric Vergne) in Santiago last year.
"My heart goes out to him; he drove a great race. It's a shame it ended up that way."
D'Ambrosio and German team mate Pascal Wehrlein failed to finish after both ran into Brazilian Felipe Nasr's crashed Geox Dragon car.
That brought out the safety car for the first time and then red flags.
When the race resumed, Britain's Oliver Rowland -- who had seized the lead at the start - slowed and Bird took the lead until he made a mistake that allowed Lotterer to go past.
The safety car was again deployed when Belgian Stoffel Vandoorne, who had been on pole position, stopped on track with a technical problem.
It came out for a third time with five minutes to go when Rowland hit the wall and damaged his rear axle, the action picking up again with two minutes to go.
Reigning champion Vergne finished 13th.
(Reporting by Alan Baldwin in London, editing by Clare Fallon)
