It meant that the Dutch driver was faster in the final phases, overtaking Mercedes' Valtterri Bottas on lap 44 prior to setting his sights Hamilton.
Red Bull's Sergio Perez, that pitted twice, finished the podium supporting Hamilton because he uttered a frustrated Bottas at the final stages.
While Mercedes will regret only pitting its drivers after, Red Bull gained from superior strategies and procured its first dual podium of 2021.
"After we left the call to perform the two-stop, fortunately at the conclusion that paid off.
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The success goes Verstappen 12 points before Hamilton from the overall standings and marked a third successive race win for Red Bull.
"We have got to get some pace, that is for certain," defending champion Hamilton told ESPN.
"You have seen that the majority of the time we dropped today was only on the straights. We have got to dig deep and learn what that is."
Although Verstappen began in rod, he immediately dropped his direct to Hamilton in the beginning of the race since he moved off the track in turn two.
However, the motorists' initial pit stops was an essential second as Hamilton, who pitted following his rival, was undercut by Verstappen on lap 21.
Chasing the very first championship title of his profession, Verstappen currently has 13 wins to his name. The F1 season resumes following weekend using all the Styrian Grand Prix in Austria.