Verstappen set a time of 1 minute, 43.184 seconds in his Red Bull to beat Ferrari driver Charles Leclerc by .043 seconds. The second Ferrari of Carlos Sainz was third, .337 seconds off the pace.
Mercedes didn't challenge for the top positions, with Lewis Hamilton seventh and Valtteri Bottas 10th.
Verstappen heads into the weekend as championship leader for the first time after winning the Monaco Grand Prix.
Leclerc took pole position in Monaco but couldn't start the race because of car damage. Leclerc has predicted Ferrari would drop back in Azerbaijan because the circuit has a long straight section.
The second practice session is later Friday.
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