The Frenchman made a quick getaway from third on the grid and demoted both Red Bulls to take control of the race, a position he maintained until the 41st of the 53-lap race.
Grosjean made good progress in his opening stints on the medium tyres, but he felt a switch to the harder compound on lap 30 suffocated any chance of victory.
"I thought today was going to be the day that my first victory was coming," he said.
"We were quick on the medium tyres, but unfortunately the car was less good on the hards."
"It was nice with Mark at the end," remarked Grosjean, "but I couldn't pull away from him on the hard tyres as they began degrading.
"In our strategy meeting, though, we never thought we could beat the Red Bulls today and we are where expected to be.
"It was nice until the end, but we caught some slow cars and they blocked me quite a lot."