Fresh from his win in Germany last weekend, Verstappen started the race from pole position after claiming his career first on Saturday, beating both Mercedes'.
However, Verstappen couldn't deny Lewis Hamilton in the race, despite holding off attacks from the Briton when they were running similar strategies in the opening and middle stints of the race.
Mercedes decided to pit Hamilton once more with 20 laps to go, with the fresher tyres allowing him to close up on the rear of the Red Bull, before completing the move around the outside of Turn 1.
"We just were not fast enough," Verstappen said. "I tried everything I could on that hard tyre to stay alive but unfortunately, it was not enough. But still second, and the fastest lap, a good weekend overall for us.
"Congratulations to Lewis for the win, he was pushing me very hard. I liked that. Today we didn't win but it was a good race and a good weekend for us.
"We were just lacking a bit of grip I guess. We tried the one-stop, they choose to do the two and that worked out well."
Verstappen now sits just seven points behind Valtteri Bottas in the drivers' standings, as F1 now enters its usual summer break, with factories set to shut down before the second half of the season.