The four-time champion, whose win in Budapest means he is now level on 41 victories with Ayrton Senna, finished ahead of the Red Bull duo of Daniil Kyvat and Daniel Ricciardo following one of the most dramatic races in recent memory.
Pole-sitter Lewis Hamilton was expected to cruise to a record fifth victory at a track in which he so often excels, but his race was blighted by a number of uncharacteristic errors and he had to settle for sixth.
It could, and quite probably should have been worse, yet Hamilton heads into the four-week summer break with an extended 21-point lead over Nico Rosberg.
The German spent the closing phase of the race battling Vettel for the win, but he crossed the line only eighth after a collision with Ricciardo in which he picked up a puncture.
There were no such concerns for his compatriot, who claimed his second win as a Ferrari driver. Vettel leapfrogged the slow-starting Mercedes pair on the run down to turn one and never looked back.
He then dedicated his triumph to Bianchi, the former Ferrari academy driver, who died earlier this month, and for whom the drivers staged a one-minute silence for ahead of the race.
“There have been some incredible ups and downs that we go through,” Vettel said pausing to clear his throat.
“This one is for Jules and especially all the people in Ferrari, and we knew that sooner or later he would have been part of our team, part of this family.”
Bianchi’s parents, Philippe and Christine, and his siblings were flown in for the race by Bernie Ecclestone and they linked arms with the drivers ahead of the race. It was a poignant moment and one which united the sport in this most tragic of circumstances.
Vettel, who along with many of his peers attended Bianchi’s funeral in Nice only days ago, added: “It was a tough start, a tough week, obviously with Tuesday, and then to think about Jules again on the grid, it was certainly very emotional and difficult to get back in the rhythm.
“I think nevertheless today is for Jules and his family and I think that’s bigger than everything else.”
On equalling Senna’s record, impressively in nine fewer starts than the legendary Brazilian, he added: “It is quite incredible and I don’t know how to put this in words.”
Bianchi’s death came nine months after his harrowing crash at the Japanese Grand Prix on October 5 and his passing cast a long shadow over the sport heading into this week’s race.
But his contemporaries vowed to race on in the Frenchman’s honour and this spectacular show was a fine tribute to a driver tipped to be a future Formula One champion.
As with the British Grand Prix earlier this month, Hamilton and Rosberg were slow off the start-line and by turn three they were behind both Vettel and his Ferrari team-mate Kimi Raikkonen.
Indeed Hamilton had slumped to fourth, and in a bid to pass Rosberg at the chicane, he slid off the track and a trip across the gravel ensued. He re-joined the circuit in 10th.
The world champion fought back to fourth before the race, which really had it all, was thrown another spectacular curveball.
Nico Hulkenberg’s Force India front wing shattered at 200mph, and while the Le Mans winner walked away unscathed, the safety car was deployed with bits of carbon fibre littering the main straight.
On the restart, Hamilton was sluggish to get away, and with Ricciardo bidding to overtake the Briton at turn one, Hamilton lost control of his Mercedes under braking and hit the Red Bull. He sustained damage to his front wing. The Briton attempted to continue but had to pit for repairs. He emerged way down the order and then was forced to serve a drive-through penalty for causing the collision.
That left him in 13th, but he benefited from a chaotic conclusion, not least Rosberg’s late tangle with Ricciardo, to finish sixth.
“I was all over the place,’ Hamilton said. ”I really don’t have any words to describe what happened. It was a really bad performance from me, one of the worst in a long time.
“I don’t know if it was a lack of concentration or what. I pushed right to the end but there were so many obstacles. It’s like there were two different directions and each time I chose the wrong one.”
Elsewhere, Max Verstappen, the 17-year-old rookie, finished a record-breaking fourth, with Fernando Alonso fifth for McLaren. Romain Grosjean (seventh), Jenson Button (ninth) and Marcus Ericsson completed the top 10.