In a race livened up by the rain after a processional 51 laps in dry conditions, Spaniard Fernando Alonso finished second for Aston Martin but a massive 27.9 seconds behind at the chequered flag.
Frenchman Esteban Ocon completed the podium completed the podium in third place for Renault-owned Alpine, their first top three finish of the season.
Mercedes' seven-time world champion Lewis Hamilton was fourth and collected a bonus point for fastest lap.
Last year's winner Sergio Perez, Verstappen's closest rival and team mate, was twice lapped on his way to 16th place after starting last. The Mexican also made five pitstops on a nightmare afternoon.
"That was a real Monaco," Verstappen said after a 78-lap race that lasted an hour and 48 minutes on a tricky street circuit where overtaking is a rare occurrence.
"It was incredibly slippery and when you are that far in the lead you don't want to push too hard but also you don't want to lose too much time so it's quite difficult in that scenario.
"I clipped the wall a few times and it was super difficult out there. But that's Monaco."
The win was Verstappen's fourth of the season, second in Monaco and 39th of his career. It also made him the driver to have won most races for Red Bull, one more than retired four times champion Sebastian Vettel.
Verstappen now has 144 points to Perez's 105 and Alonso's 93. Red Bull have 249 points in the constructors' standings with Aston Martin on 120 and Mercedes 119.
HOME HERO
Mercedes' George Russell was fifth and home hero Charles Leclerc finished sixth for Ferrari.
Alpine's Pierre Gasly, Ferrari's Carlos Sainz, McLaren's Lando Norris and teammate Oscar Piastri completed the points positions.
Verstappen led away cleanly from the start on the medium tyres, with Alonso opting for the harder compound and slotting in close behind with no change to the rest of the points positions.
If the podium ended up being the same top three as on the starting grid, the rain brought added excitement as drivers slid around the track, some getting too close to the barriers, before pitting for intermediate tyres and then full wets.
Some, such as Ferrari's Sainz, got too close to the barriers before pitting for intermediates or full wets.
Verstappen also slid scarily at Portier as he delayed his pitstop to lap 56 to coincide with the rain, while Alonso initially pitted for mediums and then had to come in again for intermediates.
"We thought to play a long game with the strategy but Max drove super well on the medium tyres and extended that first stint. We didn't have any chance and then at the end the rain put things a bit complicated out there," said Alonso.
"It was not easy and I was surprised there were no safety cars from incidents, I think everyone was doing an amazing job today to keep the cars on track."
Red Bull boss Christian Horner said Verstappen would have been under more pressure had Alonso picked the intermediate tyres straight away.
While Alonso celebrated his fifth podium of the season, and best result yet for Aston Martin, Canadian teammate Lance Stroll retired after repeated tangles with rivals.
The only other driver not running at the finish was Haas's Kevin Magnussen, whose teammate Nico Hulkenberg was 17th in the team's 150th race and collected a five-second penalty for causing a collision with Williams' Logan Sargeant.
Sargeant spent his afternoon showing that overtaking is possible on the world's most glamorous street circuit by allowing a string of drivers to get past him.
Perez pitted at the end of lap one for hard tyres to go the distance, jumping Alfa Romeo's Guanyu Zhou and Hulkenberg in the pits to move up to 18th but his race soon fell apart in a nightmare of five pitstops.
He was also lapped by Verstappen long before half way.
"I have to move on and learn from it. I cannot afford another zero in the championship," he said.
