Da Costa started the 2018/19 season opener from pole but was passed during the race by the two Techeetahs of Jean-Eric Vergne and Andre Lotterer, who had started fifth and seventh respectively.
But the two DS-powered cars were then required to serve drivethrough penalties while running one-two for exceeding the maximum permitted power while using regen - breaching article 27.9 of FE's sporting rules.
Those penalties handed the lead back to da Costa, who beat a charging Vergne to clinch a first-ever category win for BMW and the Andretti team.
Da Costa said the fact he had won despite not having the fastest car would give BMW the added motivation of trying to improve its package.
"Their [DS Techeetah] pace was impressive. That's what I told my guys," da Costa told Autosport.
“In a way, it was good that we see someone still has the upper hand on us because I’m sure these guys are going to put their head down and still work hard because that’s what I wanted.
“This is a perfect scenario for us, to win the race, win the points but have something to make us go back to work and try and improve.”
BMW yet to extract full potential of FE package
Before clinching pole and winning in Saudi Arabia, BMW had emerged as a pre-season favourite at October’s Valencia testing, during which the outfit was fastest at the end of all three days of running.
Despite a strong start to BMW's official involvement in FE, its motorsport boss Jens Marquardt is convinced the manufacturer has not been able to get the most from its car yet.
“We have to be humble here, [FE is] a very tight and strong championship and for sure we haven’t yet extracted the full potential out of our package but so has everybody else,” Marquardt told Autosport.
“We need to keep working hard with everybody involved and go from race to race."