The four-time world champion has managed only one podium in the opening five races of the season, but a sensational qualifying performance means he will start alongside pole setter Kimi Antonelli.
Verstappen held provisional pole before Italian teenager Antonelli grabbed it off him by 0.043 seconds with his final flying lap. Against all expectations, he has now given himself a shot at a third Monaco triumph.
"If you would've told me yesterday I would be on the front row, I definitely would've taken it," he told reporters.
Verstappen was a distant fifth fastest in Saturday's final practice, almost a second down on Antonelli, then things clicked in qualifying. He was second in Q1 and fastest in Q2 before a thrilling battle for pole in Q3.
"This morning, I think we had some difficulties with the car, so heading into qualifying and being up there I think was extremely positive," he said.
"Overall, of course, I'm very happy with how qualifying went, how all the laps went, even though I had to deal with all the traffic and the walls."
The unique nature of Monaco's twisty street circuit also helped him have some fun in a car that has often made him grimace this season.
"They are more on edge than the last few years, and also with the power that kicks in, driveability and shifts are all a bit different," he said.
"Once you get on top of it and get a clean lap out of it, especially in qualifying (when) you're flat-out and on the limit, it's very rewarding when it goes well."