Chilton grabbed the lead from the start, while poleman Luca Filippi (Coloni) bogged down badly and dropped to seventh.
Lotus's Esteban Gutierrez hassled Chilton through Turn 5 on the opening lap, but that left him prone to attack from behind by Fabio Leimer (Racing Engineering), although Gutierrez fended him off.
Jolyon Palmer (iSport) then grabbed third from Leimer, just before the safety car was required for a combination of first-lap accidents at the back of the field, the main offender being Rene Binder's stranded car.
At the restart, Chilton opened out a handy gap over Gutierrez and managed his advantage from there. They both pitted on lap nine, mirroring strategies of starting on the soft tyre, and then changing the rears to a fresh pair of softs.
Battle resumed after the stops, with Filippi coming back into the frame having pitted at the first opportunity on lap six. However, that strategy came back to haunt him, as Filippi's laptimes dropped off by up to 6s as his tyres went off.
Leimer, the first of the runners who started on the super soft tyre, jumped past him to finish third.
The race effectively ended under a safety car (although it did come in on the final lap) after Filippi crashed heavily at the final corner soon after making a second pitstop for new tyres. He had been into the tyre wall earlier that lap, damaging his front wing at the turn beneath the grandstand, and it appears to have come off and wedged under his car, causing him to crash at high speed.
At the front, it was status quo as Chilton had an answer for every challenge Gutierrez threw his way - and his victory never looked truly under threat at any point.
"It was a bit of a dream weekend to win like that, along with the announcement I had earlier this week," said Chilton, who is to be Marussia's reserve Formula 1 driver. "It wasn't easy, but it was the right time of the year for that win to come."
Gutierrez added: "It was a very interesting race, the tyres were very challenging to manage. I tried to pass Max at Turn 5 on the first lap, and he closed the door a little bit. I ran out of laps in the end."
Valsecchi's fourth place, ahead of title rival Luiz Razia, was more than enough to crown him as champion for DAMS. They ran nose-to-tail after Valsecchi was held up by the struggling Filippi, but he always had a pace advantage over Razia, who is confirmed as series runner-up.
Valsecchi's team-mate Felipe Nasr charged to sixth from 13th, ahead of Marcus Ericsson, with Giedo van der Garde finishing eighth to gain reversed-grid pole.
Gutierrez takes third in the championship from team-mate James Calado, who was in the thick of the battle for the bottom end of the points despite feeling unwell, until his tyres went off and he called it quits with a couple of laps to go. Fellow Briton Palmer also retired when running in sixth place.