Sutil was running third after beginning the race from sixth position but lost his way in the last six laps as Mark Webber, Kimi Raikkonen, Fernando Alonso and Lewis Hamilton all passed him.
Nico Rosberg won the race, marked by several tyre failures, while Webber and Alonso joined him on the podium in the second and third position respectively.
Nevertheless, it was third consecutive double points finish for Sahara Force India (59) as it collected eight points to increase its lead over sixth-placed McLaren (37) by 12 points.
Sutil moved up two places to fourth in the very first lap when he passed Daniel Ricciardo and Webber suffered a front wing damage to his Red Bull and was pushed back.
Disaster struck pole sitter Hamilton in the lap eight as his Mercedes' left rear tyre deflated in lap eight, ending his victory hopes in his home race.
As a result Sebastian Vettel was now leading the race and Sutil moved up to third.