Perez led Verstappen home after a tepid Azerbaijan Grand Prix, but his afternoon nearly came undone when on lap 34 he clipped the outside wall on the entry to Turn 15.
The Mexican came away unscathed but afterwards admitted his error led to a hard thump on the right-front corner of his Red Bull RB19.
"Really hard," he said about the hit. "I had a bit of luck, especially with the front right that it didn't blow up."
Starting from third, Perez quickly dispatched Ferrari's Charles Leclerc and then took the lead when Verstappen pitted on lap 10, just before the safety car came out for Nyck de Vries' stricken AlphaTauri.
Perez benefitted from the neutralisation to complete his only pitstop and remain in the lead.
And after controlling the restart the Mexican put in a composed drive on the Baku City Circuit, never coming under sustained pressure from Verstappen.
"It really worked out today for us. We managed to stay in the DRS train and we managed to keep the pressure on Max," Perez said.
"I think we had a better deg on that first stint, it was looking good already from that side.
"Then the safety car came and bunched everyone up. So, it was again another race on the hard tyres.
Source: Autosport