Red Bull's fourth one-two finish in five races dealt a blow to Mexican Perez's hopes of wresting the overall lead from the double world champion in Miami after securing pole position on Saturday.
Aston Martin's Fernando Alonso (41) finished a distant third, for the fourth time this season, after starting on the front row.
Verstappen, winner of last year's inaugural Miami Grand Prix, suffered a setback in qualifying when Ferrari's Charles Leclerc (25) crashed and denied the Dutchman a final flying lap that almost certainly would have put him on the front row after he dominated the practice sessions.
But he was immediately on the charge, moving up into fourth after 10 laps
Alonso had predicted that Verstappen would be filling his mirrors after 25 laps.
That guess proved wildly wrong as Verstappen blitzed past Alonso's Aston Martin on the 15th lap to once again leave the fight for top spot on the podium between the two Red Bulls.
Perez was the first to pit, leaving Verstappen to put in an extended run at the front before finally stopping for new tyres with just 11 laps to go and handing back the lead briefly to his Mexican teammate.
On fresher tyres, Verstappen was immediately on the prowl and two laps later he was in front of Perez.
From there it was business as usual, with the two Red Bulls easing through the final laps unchallenged for another one-two result.
Verstappen, six points clear of Perez at the start of the day, is now 14 ahead of him in the championship standings, on 119. Alonso is third on 75.
Mercedes team principal Toto Wolff (51), who on Saturday criticised the outfit's car as "a nasty piece of work", was surely better pleased with the cars' performance on Sunday, with George Russell (25) finishing fourth and seven-time world champion Lewis Hamilton (38) coming from 13th to grab sixth.
Ferrari's Carlos Sainz (28) was fifth, between the two Britons, while Leclerc was seventh in the other Ferrari.
Logan Sargeant (22), the only American on the grid, started last and found himself dropping further back after an early incident brought the Williams rookie into the pits for a new front wing. He finished last.
It was also a disappointing day for Haas, the only US-bankrolled outfit, with Kevin Magnussen (30) finishing 10th and Nico Hulkenberg (35) 15th.
Red Bull now lead the constructors' championship with 224 points with Aston Martin second on 102 and Mercedes third on 96.
There was just enough action on the 3.36-mile (5.41-km) temporary street circuit around Hard Rock Stadium to keep fans happy and quieten some of the criticism that Formula One was getting boring.
But as the circuit heads back to Europe for three grands prix in Imola, Monaco and Spain, the Red Bulls remain in a league of their own and Formula One is sure to face more talk of boring racing.
