The Red Bull star earned a maiden Monaco Grand Prix victory as Hamilton trailed in seventh, with the Mercedes team as a whole enduring a desperate day.
Valtteri Bottas was forced to retire from the race while running second when the pit crew were unable to remove a tyre, with Verstappen and fourth-placed Sergio Perez nudging Red Bull above Mercedes at the summit of the constructors' standings.
Neither Verstappen nor his team would be presumptuous enough to suggest this changing of the guard at the top of each championship is anything but potentially fleeting though, given the margins are so tight and this was just the fifth stop-off in a 23-race season.
"It's so special around here to win and to be for the first time on the podium here," Verstappen said. "It's an amazing race and you really have to keep your focus, but it's really cool.
"You never know what's going to happen, but it was all about looking after your tyres and finding a good stop gap of course. The others went earlier so that made it a bit easier for me, but it was pretty much in control.
"Of course you always want to win this grand prix. I remember when I was very little watching this grand prix and to be standing here of course I'm very proud.
"But I'm also thinking ahead. It's still a very long season, but this is a great way to continue."
Hamilton has won the last four championships and six of the last seven, while Mercedes are chasing an eighth consecutive team title.
They will have many better Sundays in the coming months, and a team statement on Twitter summed up their dismay at the Monaco outcome.
The statement said: "Tough one to swallow. This has been one of our hardest days as a team in a very long time. We have to accept it, own the failure, learn from it and move on from here."
Carlos Sainz finished second, with Verstappen keeping the Spaniard at a safe distance.
It was close to a nine-second gap at the finish, as Sainz delivered for a Ferrari side who had to stomach the pre-race blow of withdrawing pole-sitter Charles Leclerc.
Monaco native Leclerc majorly damaged his car with a heavy crash in qualifying, and despite subsequent assurances that he would be on the grid, Ferrari changed their minds just minutes before the race began, citing a problem with the left driveshaft.
As Leclerc licked his wounds, Sainz delivered a sterling drive for his first Ferrari podium finish. Even then, it felt bittersweet.
"It is a good result," said the 26-year-old Spaniard. "If you had told me before coming to Monaco that I would finish second, I would definitely have taken that.
"It's just the whole circumstances of the weekend, having Charles on pole, me missing out in qualifying yesterday on a good lap, it just maybe doesn't taste as good as it should.
"But if I reflect back in the week I will be very happy and proud of the weekend. And I think Ferrari as a team need to be proud about the team and the step they've done this year.
"When you see the other car not starting from pole, all of a sudden the responsibility relies on you, trying to salvage the weekend. I felt the team deserved at least a podium this weekend."
"I didn't think I'd be here," Norris said, at his post-race interview. "It's always a dream to be on a podium here.
"It's extra special, I didn't think it was going to happen. It's special here, so I'll cherish it."