the right. It's a good job they pulled me in," said the 2008 world champion.
The Red Bull emerged unscathed, with the team reassuring a concerned Vettel, and the German settled into third place at the end of the opening lap.
"A horrible start and then a fantastic comeback," declared the beaming Vettel, who took the lead for the first time on lap 13 after Grosjean and Webber had pitted.
The lead changed between the three over the race according to pitstops with Webber making his final stop 11 laps before the finish.
The Australian had hoped to claw back the deficit but could not get past Grosjean until the penultimate lap, by which time Vettel was nine seconds clear and out of reach.
"Mark was going through the tyres a bit quicker and getting into trouble earlier," said Red Bull principal Christian Horner. "It made a huge amount of pressure on the two-stop and would have been very difficult to beat Grosjean so we switched from two to three.
"Unfortunately we lost too much time at the end there behind Grosjean for him to have a crack at Sebastian but he (Vettel) just made the tyres last extremely well."
Kimi Raikkonen was fifth for Lotus with Nico Hulkenberg sixth in the Sauber.
Sauber's Mexican Esteban Gutierrez became the first rookie driver to score a point this season with seventh place for Sauber.
Nico Rosberg put some points on the board for Mercedes, who slipped further behind Ferrari in third place in the championship, with Britain's Jenson Button ninth for McLaren. Ferrari's Felipe Massa was 10th.