The German's victory in his Red Bull, his fifth in 11 races this season, moved him 46 points clear of Ferrari driver Alonso in the championship with 200 still available.
Di Resta dramatically crashes at Spa
The Spaniard moved up from ninth on the grid with a brilliant first few laps but could do nothing about the imperious Vettel.
Lotus's Kimi Raikkonen, another title contender, retired after a visor tear-off got jammed in one of the brake ducts, jamming some cooling channels which led to a brake failure and retirement at Spa Francorchamps.
Vettel, by contrast, looks all but unstoppable after one of the most comfortable victories of the year.
"It was a fantastic race for us," said Vettel. "From start to finish really, very good tactics - it helped the first lap to have the tow off Lewis into Eau Rouge. Once I passed him I had incredible pace and could control the race."
Vettel built a 2.8-second lead after just two laps, at which point his engineer Guillaume Roquelin told him to "save tyres", adding: "We don't need any more than this."
“The team did a great job and I'm really happy with the result”
Lewis HamiltonThird at Spa
Vettel continued to inch away and was never troubled thereafter.
Behind him, Alonso made impressive progress after qualifying in ninth place.
An aggressive first lap, including passing Red Bull's Mark Webber into Eau Rouge, put him up to fifth place, after which he passed McLaren's Jenson Button into fourth on lap four and Mercedes' Nico Rosberg into third on lap six.
Alonso then took second place from Hamilton on lap 14, after the Englishman made an error going into La Source and ran wide.
Coulthard soaked in champagne
Alonso overtook him going down the hill into Eau Rouge and then just managed to fight Hamilton off into the Les Combes chicane at the end of the long Kemmel straight, despite the Mercedes having use of its DRS overtaking aid.
Alonso inched away from Hamilton but could do nothing about Vettel as the Red Bull controlled the pace at the front and Hamilton was left to successfully fend off team-mate Rosberg and Webber in the final stint of the race.
"We had to recover some places," said Alonso. "We were not OK yesterday but everything went OK from the start and then the car had the pace to overtake some cars - then it was a little bit boring after we got into second place."
Hamilton said: "These guys were a little bit faster than me, but the team did a great job and I'm really happy with the result."
Behind them Button, abandoning a planned one-stop strategy, took sixth place ahead of Lotus's Romain Grosjean, who fended off Ferrari's Felipe Massa in the closing laps.
Force India's Adrian Sutil was ninth from Toro Rosso's Daniel Ricciardo, who passed McLaren's Sergio Perez for the final point late in the race.
The Mexican had earlier been given a drive-through penalty for forcing Grosjean off the track early in the race.
Scot Paul Di Resta was racing with Sutil and on course for a point or two, but was taken out by Williams's Pastor Maldonado in a chaotic incident at the Bus Stop chicane that also involved Sauber's Esteban Gutierrez and Sutil.
The incident started when Maldonado had a wobble at high speed coming out of the Paul Frère corner, giving Gutierrez a chance to close up and try to pass.
F1: What makes Spa so special?
The Mexican sat it out bravely around the outside of Maldonado through the flat-out Blanchimont kink and forced the Williams wide into the Bus Stop.
Rejoining, Maldonado clipped Sutil and smashed into Di Resta, breaking his right rear suspension.
Maldonado was given a drive-through penalty for causing the incident.
Vettel, though, was serenely clear of such drama as he cantered to victory, one that puts him in an increasingly comfortable position as he seeks a fourth straight world title.
Greenpeace protestors attempted to disrupt the podium ceremony by unfurling remote control banners against Arctic oil exploration. Protestors also flew over the track displaying similar banners and unfurled one on the pit-straight grandstand before the start.
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