Red Bull's Mark Webber beat Ferrari's Felipe Massa to the final podium place.
Mercedes' Lewis Hamilton fought up to ninth after dropping almost to the back when a puncture forced him to make an extra stop compared to his rivals
Alonso "extremely happy" with second
The Englishman enlivened the final few laps by passing Lotus's Kimi Raikkonen and both McLarens to haul himself up into the points.
But Hamilton is now 81 points behind Vettel in the championship, which has effectively devolved down to a straight fight between the German and Alonso.
"It was a fantastic race but you can hear the difference when you don't win here in a red suit," said Vettel on the podium, in response to booing from the Ferrari fans. "But it means you have done well and beaten the red men but it was a great team effort today.
"The race was terrific for both of us [Vettel and Webber]. We had problems with the gearboxes at the end, but I was OK because I had a good cushion."
Vettel now appears in total control of the season, just as he was of this race.
Starting from pole position, the world champion damaged his right-front tyre with a flat spot when fending off a challenge from Massa into the first corner but still managed to eke out an advantage in the opening laps.
Alonso, who started fifth, moved up at the start to fourth past Sauber's Nico Hulkenberg, who had qualified an excellent third, and then brilliantly passed Webber for third around the outside of the second chicane on lap three.
The Spaniard then passed Massa into the first chicane on lap eight but initially could do nothing about Vettel, who extended his lead by about half a second over each of the next few laps.