Verstappen is now 21 points ahead of Perez in the drivers' standings and 34 points clear of Leclerc.
The race was an unmitigated disaster for Ferrari, with both Leclerc and Carlos Sainz failing to finish the race.
Leclerc locked up on the first corner and he was forced to retire because of engine failure, while Sainz' run of horror luck continued when his car also suffered a mechanical failure.
Four cars with Ferrari-powered engines had to retire from the race which had five DNFs.
It was the worst possible result for Ferrari, who are now well behind Red Bull in the constructors' championship with Mercedes quickly making ground.
Verstappen's victory saw him break Sebastian Vettel's record for the most podiums ever for Red Bull. The Dutchman has now stepped on the podium 66 times from his 126 career races.
Daniel Ricciardo crossed the line in P8 to secure his second point finish of the season.
For much of the race, the Australian was in a tight battle with his McLaren teammate Lando Norris, who finished just behind him in ninth.
Ricciardo had better pace than Norris early in the race but McLaren refused to let him pass Norris. Ricciardo eventually got in front of Norris by staying on his hard tyres for a long first stint and pitting during a safety car period.
The F1 season continues next weekend at the Canadian Grand Prix.
