The Formula One championship leader went to the top of the board with about 10 minutes left, pipping Bottas by a narrow margin of .061 seconds and placing .167 clear of defending champion Hamilton.
Tensions between Hamilton and Verstappen have been running high since last Sunday's British GP, where Hamilton won after Verstappen crashed following contact with his Mercedes on Lap 1.
Verstappen was upset with Hamilton's jubilant celebrations while he was having checks in hospital.
Red Bull's appeal of the incident was rejected by governing body FIA on Friday and no further action was taken against Hamilton, who won at Silverstone despite being handed a 10-second time penalty.
In a remarkable near-miss during Friday's first practice, Verstappen and Hamilton almost collided in the pit lane as they exited their garages simultaneously.
In hot conditions on the sunbaked Hungaroring track, Ferrari's Carlos Sainz Jr. was fourth ahead of AlphaTauri's Pierre Gasly.
The hour-long session was briefly held up with about 20 minutes left after Japanese driver Yuki Tsunoda's AlphaTauri hit a wall. He was unhurt.
There is a second practice later Friday.
Verstappen leads the seven-time F1 champion Hamilton by eight points overall and 5-4 for wins so far. There is a four-week summer break after Sunday's race, where Hamilton will look to win in Hungary for a record-extending ninth time and fourth straight.