Perez started from pole, while Verstappen was ninth after failing to complete a lap in Saturday’s Q3 qualifying shootout.
But starting with the stiff compound, Verstappen raced effortlessly through the field on Sunday and kept his tires alive until lap 45 of 57.
Verstappen’s persistent hard pace put him almost in the lead by the final pit stop.
After switching to new medium tyres, Verstappen returned to the track behind Perez and quickly overtook his struggling teammate to claim his third win of the season.
Perez said he lost the race in the initial mid-race as the Yellowwall tires performed worse than expected and grains soon appeared.
“I think the media was really bad initially. It was worse than expected,” Perez said.
“We had really bad grain in the first stint at the initial speed. It affected our race a lot because we didn’t have much difference in the tyres.”
Perez also admitted that Verstappen beat him from a ninth-place start in the master class.
“Honestly, I think Max was very fast on the hard tyres, too, and I think I have to analyze what went wrong today because we didn’t have speed at all,” he added.
“Max was extra strong today, so it’s a well-deserved win for him.”
Verstappen said he believed his decision to start on hard ground, rather than leaving the first three rows of cars in the middle, would pay off as he did.
“We started talking about it yesterday,” Verstappen said of his winning tire strategy.
“We don’t know what the weather will be like but we are pretty confident it will pay off and luckily it did today.
“I picked car after car, and then I could stay on the hard tyres, for a long time. That’s where we made a difference today, and then at the end we had a nice little battle with Checo.
“Of course there was a bit of a setback yesterday but today we just kept calm and kept it clean. It’s always very satisfying to win a game from P9.”
Verstappen’s emphatic win came as a blow to Perez after he gained momentum after winning last week’s Azerbaijan Grand Prix.
In Miami, the reigning world champion extended his lead from six to 14 points, while also earning bonus points for the fastest lap.