Verstappen took the chequered flag 21.048 seconds clear of Perez in the 24 lap, 100-kilometre, standalone race with Ferrari's Carlos Sainz (28) finishing third.
The two Red Bulls had started on the front row, with pole-sitter Verstappen forced onto the slippery grass in wet conditions by his team mate out of turn one as the Mexican briefly took the lead.
"Good race. Just the exit of Turn One, that was not really nice. That could have been a big shunt. We need to have a chat about that. That's not OK," Verstappen said over the radio at the finish.
The pair were seen talking about the incident afterwards and appeared to have patched it up.
"I think Max was angry that I went into Turn Two. But I didn't see him there. I had a bad Turn One, so I tried to protect," said Perez, who needed a strong result after three poor races.
"Once I realised he was there, I opened the door and gave the place back into Turn Two. But it was all fine, we spoke about it."
Verstappen will also start on pole position in Sunday's main grand prix, with Perez lining up 15th after Friday's qualifying, when the Dutch driver will be chasing his fifth win in a row and seventh in nine races.
Aston Martin's Lance Stroll (24) and Fernando Alonso (41) finished fourth and fifth with Nico Hulkenberg (35) sixth for Haas, Esteban Ocon (26) seventh for Alpine and George Russell (25) bagging the final point for Mercedes.
McLaren's Lando Norris (23) was the big loser, plunging from third on the grid to ninth and one place ahead of seven-time world champion Lewis Hamilton (38), who started 18th for Mercedes.
Hulkenberg had held second place until lap 12, when his intermediate tyres went off and Perez muscled past, followed by Sainz.
The experienced German pitted for slicks, dropping to 10th but racing back to secure precious points for his US-owned team.
The top eight score points in the sprint, with Verstappen taking the maximum eight and Perez seven.
Both Red Bulls and Sainz stayed on the intermediate tyres throughout the race while others pitted for slicks as conditions improved.