The Dutchman had expected to need rain to take victory but Kimi Raikkonen’s engine failure before the race even started gave him the chance to attack pole-sitter Lewis Hamilton.
Verstappen, who turned 20 on Saturday, dived down the inside of Turn 1 on Lap 4 to get past Hamilton and never gave up the lead.
The Brit meanwhile quickly became more concerned with title rival Sebastian Vettel, who had started last because of engine problems on Saturday which did not allow him to set a time.
The German, who had comfortably the fastest car on race day, sliced through the field methodically to minimise the damage of Saturday’s disaster.
But despite Mercedes’ struggles for race pace, Vettel could not quite get back on level terms with Hamilton, allowing him to open up a 34-point lead in the title race.
Verstappen has endured an “annus horribilis” at Red Bull, with seven retirements and only one podium finish before Malaysia.
And he admitted beforehand that in dry conditions, he did not expect to be challenging at the front of the race.
Raikkonen in the Ferrari, starting second, should have been the major threat but he was pushed off the grid just minutes before the race start with a turbo problem that left him unable even to start the race.
It gave Verstappen a clear run down to Turn 1 and he got ahead of team-mate Daniel Ricciardo despite the Australian veering across the track to cover off the move.
The 20-year-old quickly had Hamilton in his sights as Mercedes’ fears about their lack of race pace came to fruition.
Verstappen needed just three laps and one corner to get past the Brit, who later admitted he hadn’t fought too hard for the position, knowing that finishing ahead of Vettel was more important.
Much further back, Vettel wasn’t exactly tearing through the field, but he did make steady progress. The German was even looking at catching Hamilton himself for a brief period but instead he had to settle for fourth place after Ferrari made him back off due to an overheating engine behind Ricciardo.
Adding injury to the insult of allowing Hamilton to take a 34-point lead, Vettel finished the afternoon on three wheels after colliding with Lance Stroll on the slowdown lap.