The Red Bull team of Perez and teammate Daniel Ricciardo won the Monaco Grand Prix.
After the start was delayed for an hour because of rain, the Mexican rose from third to the lead.
Red Bull's strategy vaulted Max Verstappen from fourth to third, behind Carlos Sainz and ahead of Charles Leclerc.
Verstappen's lead was extended to nine points.
Perez is only six points behind Leclerc after a strong weekend in which he outpaced Verstappen and drove superbly in the race to deliver on Red Bull's strategy calls.
After the race, Ferrari lodged protests against both Perez and Verstappen because they crossed the white line on the exit of the pit lane.
The results of the Red Bull drivers are under threat if they are upheld.
After taking pole position on Saturday, Leclerc saw a comfortable lead turn into a fourth place finish within four laps.
After the race was red-flagged for a second time after 30 laps because of a heavy crash by Mick Schumacher's Haas at the Swimming Pool section of the track, Leclerc asked whether they would run to the end from their current positions.
When told they would, Leclerc voice heavy with sarcasm, said: "Oh, perfect."
He said nothing over the team radio at the end. The season is long, but we can't do that.
The race had to be stopped after 64 of the 77 laps because of time restrictions in the rules, but Perez held on from Sainz, Verstappen and Leclerc.
The race was one hour and five minutes late and all cars were forced to use the extreme wet tyres before the race director decided it was safe to let the cars out.
After 10 laps, Leclerc was four seconds in front of Sainz, Perez and Verstappen, and 5.3 in front of Perez when he stopped for intermediate tires.
Pierre Gasly's Alpha Tauri was the one who took the cue from Red Bull and went for inters after the start.
The Frenchman set the fastest times once in free air.
Sainz refused to switch to dry-weather slicks after Perez's pit stop because he wanted to stay out on the wets.
Two laps after Perez stopped, Leclerc and Verstappen also stopped for inters, but such had been Perez's pace, Leclerc emerged from the pits behind the Red Bull, albeit still ahead of Verstappen.
Soon that would change.
Three laps after stopping for intermediates, Leclerc was in again, as Ferrari pitted both cars for hard-compound slicks, bringing Sainz in from the lead and stacking Leclerc behind him.
Perez was in the lead by the time Sainz came back, so he was in the lead when Sainz came back.
Red Bull brought Verstappen in for his hard tyres, and his in lap combined with Leclerc's struggles with tyre temperature vaulted him into third place.
The race was stopped after five laps. The result was already decided when it started again.
Sainz began to put heavy pressure on Perez, with Verstappen and Lerclerc right behind him, as the leader struggled with tyres he had damaged with a lock-up on the first lap after the restart, and which were also graining.
Monaco was a place where it was almost impossible to overtake and they stayed in line astern to the flag.
George Russell took fifth place in the Mercedes after a strong weekend, beating McLaren's Lando Norris, Alpine's Fernando Alonso and the second Mercedes of Lewis Hamilton.
The final points places were taken by Alfa Romeo's Valtteri Bottas and Aston Martin's Sebastian Vettel after Alpine's Esteban Ocon was fined five seconds for a collision with Hamilton earlier in the race.
The start of the race was delayed by an hour after a shower.
There were questions as to whether it could have started in the conditions that existed at the scheduled start time.
The track was unsafe for racing after a heavy rain started about 15 minutes after it had been delayed.
There were questions as to whether the second red flag was necessary, and whether the race should have been restarted sooner.
There is a two week break before two races in quick succession, first in Azerbaijan and then Montreal.
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