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The 23-year-old Dutch driver started the day 14 points behind Mercedes' seven-time world champion Hamilton and ended it four clear.
Verstappen finished second at the Algarve circuit with Mercedes' Valtteri Bottas completing the podium, and taking a bonus point for the fastest lap, after starting from pole position.
Verstappen, who passed the Briton with four laps to go only to have to hand back the lead for exceeding track limits, finished a mere 0.745 seconds behind after starting on pole position.
Mercedes won 13 of the 17 races last season, and have taken both titles for the last seven years, while once-dominant McLaren have not won a race since 2012.
The season will end with the Abu Dhabi Grand Prix at the Yas Marina track on December 13. It is unclear whether Hamilton will take part.
French driver Romain Grosjean had a miraculous escape from a fiery first-lap crash that ripped his car in two.
Hamilton, celebrating his seventh win of the season, is now 69 points clear of the Finn in the standings with six rounds remaining.
The 33-year-old German replaces Mexican Sergio Perez at the team formerly known as Racing Point.
Hamilton's win at a sunny Spa-Francorchamps circuit on Sunday, which left him two short of Michael Schumacher's record tally of 91 victories, was his fifth in seven races.
Formula One's 10 teams have committed to the sport until at least the end of 2025.