Vettel's Red Bull teammate, Mark Webber of Australia, was third.
As he's done twice before, Vettel spun his car through several doughnuts after the checkered flag, a move that has drawn fines from the sports' governing body.
Vettel hardly seemed to care, however, telling his crew over his radio, "We have to remember these days. I love you guys. We have an incredible team spirit. I'm so proud of you. I love you.''
Vettel later appeared to wipe away tears while standing on the podium while listening to the German national anthem.
The 26-year-old Vettel made his Formula One debut at 19 in the 2007 U.S. Grand Prix in Indianapolis and now has an American title that escaped him last year. Vettel led the 2012 race in Austin most of the way until Lewis Hamilton passed him with 14 laps to go and went on to win. Vettel had called that a frustrating result and ruthlessly dominated the field this time.
He avoided any danger in the treacherous first corner that pushes the drivers up 133 feet out of the start and into a blind turn left back down the hill. Typical of his quick starts, Vettel immediately started putting distance between himself and the other cars with the initial burst.
Webber, who had barely missed winning pole position on Saturday, had a terrible start from No. 2 as Grosjean and Mercedes' Hamilton both nosed ahead and pushed him into fourth barely seconds into the race.
The only crash in the race came in the first lap. Sahara Force India's Adrian Sutil was knocked out when he bumped tires with Sauber's Esteban Gutierrez, sending Sutil nose first into the wall and putting the race almost immediately under a yellow flag. Sutil was able to climb out of the car unhurt.
Webber fought back from his bad start to overtake Hamilton, who finished fourth. Webber pushed Grosjean through several tense laps late but couldn't find a chance to slip into second as Grosjean held him off.
For Grosjean, it was another impressive result in the second half of the season with his fourth podium finish of the year and third in six races.
For the 37-year-old Webber, next week will be his last race in Formula One as he's leaving the series after 12 years, seven of them with Red Bull, a span that has featured some tense moments with teammate Vettel. Webber has nine career victories but none this year despite two starts from pole position and three more from the No. 2 position.
The only dangerous incident came in the first lap. Sahara Force India's Adrian Sutil was knocked out when he bumped tires with Sauber's Esteban Gutierrez, sending Sutil nose first into the wall and putting the race almost immediately under a yellow flag. Sutil was able to climb out of the car unhurt.
- AP
