After polesitter Felipe Nasr made a terrible start, Simon Trummer leapt into the lead in his Rapax machine.
From sixth on the grid, Palmer took advantage of Stefano Coletti stalling ahead of him to jump up to second at the first corner.
A lap later, Palmer passed Trummer for the lead, and he controlled that to the finish, winning by 0.8s in a race of tyre management in 28C desert heat.
Vandoorne: I had to dominate GP2
"I'm absolutely delighted," said Palmer. "We did a lot of homework last night on starts and tyre deg and we nailed them both."
Trummer held off Carlin's Julian Leal for second, which was his first podium in the series.
Nasr recovered to finish fourth, passing Adrian Quaife-Hobbs in a terrific late-race battle, during which they swapped the position three times.
Stephane Richelmi also passed Quaife-Hobbs on the final lap, but he is under investigation for a robust move on Arthur Pic earlier on.
Quaife-Hobbs finished sixth, ahead of a charging Mitch Evans and Rene Binder. Pic finished ninth.
Yesterday's debut race winner Stoffel Vandoorne was one of many to make a poor start, dropping from eighth to 11th, and as he battled his way back through he broke his front wing hitting Daniel de Jong at Turn 4.
Vandoorne had already suffered a pre-race drama when a bodywork panel on his chassis fell off on an installation lap, and he trailed home 22nd.
Results to follow...
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