The Racing Engineering driver won from pole position, but his near one-second advantage from qualifying did not quite translate into the easy victory run he might have expected.
Although fellow front-row qualifier Marcus Ericsson started from the pitlane after stalling on the dummy grid, a tentative start and opening few corners exposed Leimer to attack from hard-charging points leader Stefano Coletti.
Having forced Leimer to defend at Turn 4, Coletti's Rapax car drew alongside through Turns 5/6, but was unable to pass.
After that scare, Leimer was able to settle down and pull out a gap over his pursuer.
Leimer led by over 3s when he pitted, but his next threat came from those who started on the hard tyre and were running a long first stint compared to the frontrunners, who had mainly started on the softs.
In the midst of heavy, slow-paced traffic, Leimer's hard-fought lead over Coletti quickly dwindled to as little as 1.3s, but some brave moves - including passing the battling Mitch Evans and Kevin Giovesi in one move at Turn 4 - restored his breathing room.
Coletti then got delayed by the same traffic jam, and the gap was soon back to over 3s.
With Adrian Quaife-Hobbs the last of the hard-tyred starters to pit, having led for 10 laps, the way was clear for Leimer to cruise to victory by 1.9s from Coletti.
Caterham's Alexander Rossi finished his first main GP2 Series race in a superb third place, his decision to stop early to switch from softs to hards paying big dividends in terms of track position.
He jumped ahead of Jolyon Palmer, who had passed had him on lap two, as well as Sam Bird and Felipe Nasr, who both suffered dreadful pitstops.
Nasr finished right on Rossi's tail in fourth, having passed Carlin team-mate Palmer at Turn 4 with three laps to go.
Bird's pace dropped off badly in the closing stages, but he held on to sixth for Russian Time, ahead of a great late-race fight between Quaife-Hobbs and Bird's team-mate Tom Dillmann, both of whom started on the harder tyre.
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