Vettel is still ahead of the Dutchman 4-2 on championships won but Verstappen has plenty of time on his side to match or surpass that mark with a third title surely on its way this season.
Verstappen is 39 points ahead of Mexican teammate and closest rival Sergio Perez after winning four of six rounds with 16 remaining to be raced.
"If you have a good car for a while you can break these kinds of numbers," the champion said when reminded about the team record.
"But yeah, it's great. I mean, I would have never thought that I would be in this position in my career. When I grew up I wanted to be a Formula One driver and winning these races is amazing.
"It's better than I could have ever imagined, for sure."
Verstappen joined Red Bull mid-season in 2016, after 23 races for sister team Toro Rosso (now AlphaTauri), and took his first win on his debut in Barcelona.
Vettel won 53 races in total - one of them with Toro Rosso and 14 with Ferrari.
Verstappen's victory on Sunday was his second in three years on the streets of Monaco and Red Bull's third in a row, but the seeds were sown with a qualifying lap on Saturday that will rank as one of the sport's greatest.
In the end, he led all the way - a normal state of affairs in Monaco where overtaking is a rare feat - and took the chequered flag 27.921 seconds clear of Aston Martin's second-placed Fernando Alonso.
"With that victory, he becomes the most winningest Red Bull driver," said team boss Christian Horner. "He passes Sebastian's record which is an incredible achievement.
"He's obviously at the top of his game and driving incredibly well."
Perez knows he cannot afford another zero weekend
Sergio Perez started the Monaco Grand Prix weekend hoping to repeat last year's win and it turned into a nightmare he cannot afford to repeat.
The Red Bull driver lined up last on the grid after crashing in qualifying and finished 16th after a series of collisions, five pitstops and twice being lapped by his winning teammate Max Verstappen.
"I think we’ve paid the price for my mistake (in qualifying)," Perez told reporters. "That's been very costly.
"I just have to apologise to my whole team. It is unacceptable to have this kind of mistake. I just have to move on, learn from it, and I cannot afford another zero in the championship."
Perez pitted after the first lap, planning on going to the end of the race on hard tyres but that was soon blown out of the water.
While he gained two places in the pitstop, he hit traffic and then tangled with Aston Martin's Lance Stroll when he tried to pass as Verstappen lapped them both.
He had to pit for a new front wing after a collision with Haas's Kevin Magnussen and was dealt another setback when it rained.
There were further incidents, one with Mercedes' George Russell that again damaged his front wing and a brush with the wall that damaged his car.
"We took a really aggressive strategy, we stopped on lap one and you could see his pace in free air," said Horner.
"He actually got back within a pit window of (Alpine's third-placed) Esteban Ocon but then (Williams' Logan) Sargeant and the slow cars starting to struggle and of course, you can't overtake.
"And then he got involved in a kerfuffle with Russell and damaged the front wing. It was just one of those weekends where nothing went his way.
"I would think for him the sooner he gets to Barcelona the better.
"In some ways, it takes pressure off because he's got nothing to lose now."
