Vettel, who also won the previous race in Singapore, is moving within sight of a third straight title — something only previously achieved by Juan-Manuel Fangio and Michael Schumacher — with five races left.
"It was an important step today," Vettel said. "There is still a long way to go. I don't know what happened behind me today but Alonso was very unlucky. We never know what is going to happen in the next race so it was important to take points today."
Alonso's Ferrari teammate Felipe Massa was second, 20.6 seconds behind Vettel for his first podium since Korea in 2010, putting in a performance that should boost his chances of retaining his place in the team.
Sauber's Kamui Kobayashi delighted home fans by taking third place — holding off a strong late challenge from McLaren's Jenson Button — for his first-ever F1 podium, becoming the first Japanese driver on a podium here since 1990.
The race got off to a tumultuous start with a series of collisions in the first corner sequence. Alonso made contact with the Lotus of Kimi Raikkonen and appeared to sustain a puncture, fishtailing off the track and the car stalled, leaving a disconsolate Alonso to trudge back on the short walk to the pits.
Also on the first bend, Lotus' Romain Grosjean rammed into the Red Bull of Mark Webber, putting the Australian to the back of the field after starting from second. Grosjean was given a drive-through penalty for causing the collision, and given he was suspended for a race for doing the same in Belgium, the Frenchman may well receive further such punishment.
Also in the first corner, Mercedes' Nico Rosberg came together with Williams' Bruno Senna, ending the German's race.
Vettel avoided all the trouble behind him at the first turn, and quickly established a comfortable lead.
Massa overtook Kobayashi after the first set of pitstops and managed to close the gap slightly but Vettel maintained a strong lead to the checkered flag.
Vettel blocked Alonso during the final moments of qualifying on Saturday when the Ferrari driver was arriving at the chicane. Race officials reviewed the incident and reprimanded Vettel but allowed him to maintain pole position. That decision may have been a factor in Alonso's aggressive start.
Sauber driver Sergio Perez's day came to an end when he spun off the track on the 19th lap trying to pass Lewis Hamilton at the hairpin turn. Perez will replace Hamilton next season at McLaren as the Briton moves to Mercedes.
With the winner decided early on, the focus for many of the fans became third place where Kobayashi was battling it out with Button, who won here last year.
Kobayashi, who started third on the grid, prevailed by half a second to become the first Japanese since Aguri Suzuki in 1990 to celebrate on the podium in front of home fans.
Hamilton finished in fifth, 20 seconds off Button, and in front of a chain of cars fighting out the lower points positions. Raikkonen took sixth ahead of Force India's Nico Hulkenberg, with Pastor Maldonado of Williams eighth and Webber recovering for ninth. Toro Rosso's Daniel Ricciardo held off Michael Schumacher of Mercedes to take the last point.
In the drivers' championship, Alonso and Vettel look like fighting out the title. Raikkonen is 33 points behind Vettel in third and five points in front of Hamilton. Webber and Button are 59 and 63 points off the lead respectively.
Red Bull extended its lead in the constructors' championship to 42 points ahead of McLaren, with Ferrari a further 20 points behind.