The victory also made it a British double in Diriyah, with Envision Virgin Racing’s Sam Bird winning Friday’s season-opener.
Bird was unable to carry the momentum, crashing out with 27 minutes remaining after a tangle with Jaguar’s Mitch Evans, and slipped to third in the overall standings and a point behind Mercedes driver Stoffel Vandoorne.
Sims has 35 points to Vandoorne’s 27.
The Briton’s German team mate Max Guenther finished second in Saturday’s race with Brazilian Lucas di Grassi third for the Audi Sport ABT team.
DS Techeetah’s reigning champion Jean-Eric Vergne failed to score for the second race in a row, ending up 11th after Friday’s retirement.
“That was pretty much a dream race,” said Sims, who started both races from pole position. “We seemed to execute everything really well, made the right decisions at the right times. It just all went smoothly today.
“Crossing that line was an amazing feeling. All of last season and yesterday, I feel there’s so many lessons that we’ve learned.
“They’ve stuck with me through the tough times last year and now to deliver a win is pretty cool,” added the bespectacled 31-year-old.