Verstappen has outscored Hamilton by 23 points over the last three races, two of which have been won by the Dutchman, and hopes of the Red Bull man launching a late title bid were raised as he took his first career pole at the Hungaroring.
Bottas remains Hamilton's closest rival in the standings, 41 points adrift, and he too managed to get ahead of the five-time world champion.
With overtaking chances at a premium in the Hungaroring, Hamilton faces an uphill challenge to avoid having his standings lead trimmed on Sunday.
"Naturally we're always targeting first," he said. "Max did a great job, and so did Valtteri.
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