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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.
They are reserved for the house's selected and most faithful clients, those who already own one or more Ferraris.
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.
"I wanted that MSC," the 21-year-old Haas driver told reporters during pre-season testing in Bahrain ahead of his F1 race debut there on March 28.
The launch, presented online by "Quantum of Solace" actress Gemma Arterton, played up the 108-year-old marque's connection to the fictional British secret agent as the Silverstone-based team started a new era.
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.
F1 is still considering a Saturday sprint format, according to new head Stefano Domenicali.
Campos Racing, who have teams in the Formula Two and Three support series, said in a statement on Thursday that their founder had passed away from "sudden coronary disease".
French driver Romain Grosjean had a miraculous escape from a fiery first-lap crash that ripped his car in two.