The Briton, who qualified fourth, led from the first corner as all three of the drivers ahead of him had dramas.
Polesitter Carlos Sainz Jr was wheeled off the grid at the start of the formation lap as his DAMS team worked on an electrical problem, while a fast-starting Stevens was then able to catapult himself into the lead as Will Buller and Luca Ghiotto struggled off the line when the lights went out.
Stevens was never headed after that, as he set about gradually increasing his lead over ex-DTM racer Roberto Merhi throughout the race.
Merhi took a relatively comfortable second ahead of Red Bull junior Pierre Gasly, who was one of several drivers placed under investigation for running straight on at the first chicane on the opening lap.
Gasly lost touch with Merhi as he battled with Nikolay Martsenko, who briefly took third place from the Frenchman before falling back on lap 17 of the 24 after an off at Lesmo 2.
That put the Russian under pressure from a recovering Buller in the closing stages, and the Briton stole fourth place on the final lap.
Their scrap came home a long way ahead of the rest of the field, as Oliver Rowland spent the majority of his race fending off attacks from Marlon Stockinger.
The rookie got some respite when his team-mate Sergey Sirotkin started challenging Stockinger, eventually getting through with a robust pass on the outside into the second chicane.
However, Stockinger got the place back when Sirotkin locked up and went off at the Ascari chicane. The Russian ran out of time to launch another bid to get ahead.
The early-race action was punctuated by a frightening accident involving Marco Sorensen and Jazeman Jaafar.
The pair clashed on the start/finish straight at the end of the opening lap, sending the Dane's Tech 1 car upside down and into the pitwall.
Sorensen, who appeared to move across on Jaafar, was able to walk away from the crash, which will be investigated by the stewards.
Results - 24 laps:
Pos Driver Team Time/Gap
1. Will Stevens Strakka 42m23.207s
2. Roberto Merhi Zeta Corse +6.870s
3. Pierre Gasly Arden +11.760s
4. Will Buller Arden +17.994s
5. Nikolay Martsenko Comtec Racing +18.423s
6. Oliver Rowland Fortec +25.440s
7. Marlon Stockinger Lotus +25.943s
8. Sergey Sirotkin Fortec +26.398s
9. Zoel Amberg AV Formula +31.784s
10. Meindert van Buuren Pons Racing +32.391s
11. Matias Laine Strakka +32.599s
12. Pietro Fantin Draco +35.580s
13. Oliver Webb Pons Racing +37.675s
14. Roman Mavlanov Zeta Corse +47.549s
15. Norman Nato DAMS +1m06.012s
16. Luca Ghiotto Draco +1 lap
17. Matthieu Vaxiviere Lotus +3 laps
18. Carlos Sainz Jr DAMS +3 laps
Beitske Visser AV Formula 19 laps
Marco Sorensen Tech 1 1 lap
Jazeman Jaafar ISR 1 lap
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