Rapax driver Coletti started from pole for the first Feature race of 2013, but had to defend stoutly from the fast-starting Leimer, who rocketed his Racing Engineering car from fourth to second by the first corner.
This duo was over five seconds clear of the field by lap three, as front-row starter James Calado of ART got into a huge battle early on with Carlin's Felipe Nasr and then Arden's Mitch Evans.
Despite running third for the first few laps, Evans, who was suffered from food poisoning, tumbled down the order and would finish 10th.
Coletti was clearly struggling with tyre wear more than Leimer on the opening stint on soft rubber, and pitted at the end of lap six.
Leimer stayed out for a further four laps, but still rejoined behind Coletti, who had been able to use his fresh hard-compound rubber to good effect to keep track position.
Stopping earlier was always going to come back and haunt Coletti. After 20 laps on this set of tyres, Coletti had a big lock-up into Turn 14. Leimer was unable to get past him immediately, as he lacked straightline speed on the long drag to the final corner, but a clever switchback move at the exit of Turn 4 on lap 27 put him ahead.
In clear air, Leimer was able to dip under the 1m50s bracket straight away and he romped away to two-second victory. The duel between the battling leaders allowed Calado to catch them up, and he pounced on Coletti.
After a big battle into the last corner on lap 27, during which he grabbed the place but ran wide at the exit, Calado finally nailed the pass at Turn 1 on the following tour.
But Leimer was 2.7 seconds ahead by then, so Calado had no chance of catching him, and the Swiss driver recorded his third-ever victory in the series.
"I knew the car was good," said Leimer. "And I think this result shows we can fight for the championship. It's really nice to win the first race."
Behind Coletti, who trailed home almost 10s behind Calado such was his tyre degradation by the closing laps, Nasr finished a distant fourth, ahead of the second Racing Engineering car of Julian Leal.
The first car home that started on hard-compound tyres was Carlin's Jolyon Palmer. He stormed through from 22nd on the grid to lead the middle part of the race for nine laps, as the soft-shod starters pitted.
Once Palmer made his stop on lap 21, switching to the soft rubber himself, his pace was such that he rejoined sixth, a position he maintained to the finish despite front-left wing damage.
The charging Sam Bird ran a similar strategy, and would have finished much higher but for a drive-through penalty for failing to slow sufficiently under yellow flags - one of six drivers to be penalised.
He took fastest lap and finished seventh after a barnstorming pass on Evans and Stephane Richelmi at Turn 1 on lap 24.
Richelmi (DAMS) finished eighth ahead of Simon Trummer (Rapax) and Evans.