The Red Bull driver finished second to take a six-point lead in the championship ahead of Lewis Hamilton who finished fifth voicing frustration with his Mercedes' team strategy.
"From my side, probably one of the best races I've ever had," said Bottas after his 11th career win.
Sergio Perez, in the other Red Bull, took third with Ferrari's Charles Leclerc in fourth.
"It wasn't easy today," said Verstappen.
"The track was very greasy, we had to manage the tyres the whole race so couldn't really push.
"Just seemed Valtteri had a bit more pace, could look after the tyres all race. Happy to finish second in these conditions, it's easy to get it wrong so you drop back."
Hamilton was quickest in qualifying but had to start the race in 11th because of a grid penalty incurred for changing his engine.
The seven-time champion gained two places on the opening lap before picking his way up to fifth where he was held up by Perez, the two of them dicing at the end of lap 35 in some classic wheel-to-wheel racing.
As the other cars came in to change their tyres Hamilton stayed out, moving up to third and looking good for the podium.
Hamilton declined the initial call to come in for fresh tyres but finally acceded to the Mercedes team instructions, boxing eight laps from the end.
It cost Hamilton two places as Perez and Leclerc flew on ahead and the Englishman did not hide his frustration over the radio.
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