Verstappen, who celebrated his 20th birthday on the eve of the race, put the disappointments of seven retirements in 2017 firmly behind him to claim Red Bull's second win of the season.
Lewis Hamilton quickly conceded the lead to Verstappen after starting from pole, but finished second to extend his title lead over fourth-placed Sebastian Vettel to 34 points with five rounds remaining.
Vettel, who started from the back of the grid in his Ferrari after engine problems ruined his qualifying session, produced the drive of the day, but could not dislodge Verstappen's teammate Daniel Ricciardo from the final spot on the podium.
To cap a weekend of setbacks for Ferrari, Kimi Raikkonen, who qualified in second, was unable to take part after a fault developed in his car ahead of the formation lap.
That left Hamilton with an easier task to maintain his advantage off the start, but on the fourth lap of 56 he was overtaken by the charging Verstappen, who easily maintained his lead until the finish of a largely uneventful race.
The biggest drama was reserved until after the finish as Vettel's car was clipped by the Williams of Canadian teenager Lance Stroll, wrecking the back wing and leaving the German to hitch a lift back to the pits.
"That's incredible," complained Vettel. "Stroll wasn't looking where he was going."
Stroll had finished a fine eighth. "It's just a very strange incident, it wasn't intentional from either of us," said the 18-year-old.
Verstappen, who many tip to be a future F1 world champion, realized he was in with an excellent chance of victory, particularly after Raikkonen's exit and with Hamilton eying the title.
"He (Hamilton) had more to lose than me in the championship, so I went for it in Turn One and from there I could do my own race," he said.
Verstappen had to fend off an attack from Hamilton's Mercedes teammate Valtteri Bottas on the first corner to defend his second place, but that was to prove the high point of the day for the Finn, who slipped right off the pace in fifth place.
With Bottas struggling, it left Hamilton with a lonely task to repel the challenges of Ricciardo and later Vettel, but he was satisfied with his result after a difficult weekend for the usually dominant Mercedes team.
"It was a tough race," he admitted. "They (Red Bull) had the upper hand on us today."
He will now head to Suzuka for the Japanese Grand Prix next week with a solid, but not unassailable advantage over Vettel, with a maximum of 125 points up for grabs in the remaining races of the F1 season.
Sunday's race marked the final edition of the Malaysian GP, which has been staged since 1999, but the country's prime minister, Najib Razak, hinted that it could return at some point.
Razak told reporters that he did not want the Sepang circuit to become a "white elephant" and did not rule out F1 coming back, "if the economics were right."