Red Bull's Verstappen passed pole-sitter Lewis Hamilton into Turn 1 on lap four at Sepang and from there controlled the race to take the second win of his career.
Hamilton finished 12.7 seconds adrift in second, with Red Bull's Daniel Ricciardo completing the podium in third.
Ferrari's Vettel, running a new spec engine, hunted Ricciardo down in the closing laps, but had his challenged cooled when his team told him to back off because of concern over engine temperatures.
In a bizarre incident on the slow-down lap, Lance Stroll crashed into Vettel, causing significant damage to the left rear of Vettel's Ferrari.
"That's impossible," said Vettel on team radio. "Stroll's not looking where he's going."
Stroll told his team: "Vettel just drove into the side of me."
Vettel, who hitched a lift back to pits on the side of Pascal Wehrlein's Sauber and took his steering wheel with him, now trails championship leader Hamilton by 34 points with five races to go.
There was drama before the start as Kimi Raikkonen, who was due to start second, suffered a turbo problem, and though the team tried to rectify it, they were unable to do so before the race began, forcing him into retirement.
Hamilton got away cleanly from pole, with Verstappen holding off a fast-starting Valtteri Bottas to take second, with Ricciardo slotting into fourth.
Verstappen then set about closing the gap to Hamilton and once he was in DRS range, the Red Bull driver was able to launch a move down the inside at Turn 1.
His teammate Ricciardo hustled Bottas, getting alongside around the outside of Turn 1 and though the Finn held on around the outside of Turn 2 to get the place back, Ricciardo has the momentum to pass into Turn 4.
Further back, Vettel was making strong progress, climbing up to 12th by lap two and eighth by the end of lap 11.
Hamilton was the first of the frontrunners to pit for the first and only time at the end of lap 26, the Mercedes driver swapping supersofts for a fresh set of soft tyres.
Race leader Verstappen reacted the next lap, taking the softs, too, and rejoining ahead of Hamilton.
Ricciardo inherited the lead, but relinquished it to Verstappen, who led Hamilton by around nine seconds, when he pitted two laps later.
Verstappen rolled the pace at the front to take victory, with Ricciardo gradually closing the gap to Hamilton but running out of laps to get close enough to launch an attack.
Vettel ran as high as fourth, before dropping back to sixth after his stop. The German than fought back up to fourth and had a look at a pass on Ricciardo only to have the door slammed shut.
The Ferrari driver's challenge subsequently wilted in the closing stages and he ended up fourth.
Bottas finished a lonely fifth with Force India's Sergio Perez having a clean race to take sixth.
Stoffel Vandoorne made a strong start, rising up to fifth from seventh, but did not have the pace to match Vettel and Perez and ended up seventh for the second successive race.
Lance Stroll was eighth, ahead of teammate Felipe Massa, who came out on top in a feisty battle for ninth with Esteban Ocon.
It was a scrappy race for Ocon, who was sandwiched between Massa and teammate Perez at the start, leading to him picking up a puncture.
He also collided with Carlos Sainz at Turn 1, pitching him into a spin, and then found himself on the grass when battling Massa later in the race.
Renault's Jolyon Palmer had a scrappy race, including two spins in close succession, the second of which was the result of contact with Kevin Magnussen, and ended up 15th, one place ahead of teammate Nico Hulkenberg.
Sainz was running in the points when he was forced to retire with an engine problem, while rookie Toro Rosso teammate Pierre Gasly finished 14th in his first grand prix.
29 Sep01 Oct 2017Sepang International Circuit, Kuala Lumpur
|1||33||Max Verstappen||RED BULL RACING TAG HEUER||56||1:30:01.290||25|
|3||3||Daniel Ricciardo||RED BULL RACING TAG HEUER||56||+22.519s||15|
|6||11||Sergio Perez||FORCE INDIA MERCEDES||56||+78.630s||8|
|7||2||Stoffel Vandoorne||MCLAREN HONDA||55||+1 lap||6|
|8||18||Lance Stroll||WILLIAMS MERCEDES||55||+1 lap||4|
|9||19||Felipe Massa||WILLIAMS MERCEDES||55||+1 lap||2|
|10||31||Esteban Ocon||FORCE INDIA MERCEDES||55||+1 lap||1|
|11||14||Fernando Alonso||MCLAREN HONDA||55||+1 lap||0|
|12||20||Kevin Magnussen||HAAS FERRARI||55||+1 lap||0|
|13||8||Romain Grosjean||HAAS FERRARI||55||+1 lap||0|
|14||10||Pierre Gasly||TORO ROSSO||55||+1 lap||0|
|15||30||Jolyon Palmer||RENAULT||55||+1 lap||0|
|16||27||Nico Hulkenberg||RENAULT||55||+1 lap||0|
|17||94||Pascal Wehrlein||SAUBER FERRARI||55||+1 lap||0|
|18||9||Marcus Ericsson||SAUBER FERRARI||54||+2 laps||0|
|NC||55||Carlos Sainz||TORO ROSSO||29||DNF||0|
|4||Daniel Ricciardo||AUS||RED BULL RACING TAG HEUER||177|
|6||Max Verstappen||NED||RED BULL RACING TAG HEUER||93|
|7||Sergio Perez||MEX||FORCE INDIA MERCEDES||76|
|8||Esteban Ocon||FRA||FORCE INDIA MERCEDES||57|
|9||Carlos Sainz||ESP||TORO ROSSO||48|
|11||Felipe Massa||BRA||WILLIAMS MERCEDES||33|
|12||Lance Stroll||CAN||WILLIAMS MERCEDES||32|
|13||Romain Grosjean||FRA||HAAS FERRARI||26|
|14||Stoffel Vandoorne||BEL||MCLAREN HONDA||13|
|15||Kevin Magnussen||DEN||HAAS FERRARI||11|
|16||Fernando Alonso||ESP||MCLAREN HONDA||10|
|18||Pascal Wehrlein||GER||SAUBER FERRARI||5|
|19||Daniil Kvyat||RUS||TORO ROSSO||4|
|20||Marcus Ericsson||SWE||SAUBER FERRARI||0|
|21||Antonio Giovinazzi||ITA||SAUBER FERRARI||0|
|22||Pierre Gasly||FRA||TORO ROSSO||0|
|3||RED BULL RACING TAG HEUER||270|
|4||FORCE INDIA MERCEDES||133|