Verstappen skated around the Miami Autodrome on his only lap in the top 10 shootout, but his nearest rivals also struggled to improve on their SQ2 times despite bolting on softer tyres for the final shootout.
McLaren's Lando Norris particularly looked to have missed a chance for a second consecutive sprint pole, his table-topping SQ2 faster than Verstappen's pole-winning effort of 1m27.641s.
Instead, Verstappen found four tenths to gap Ferrari's Charles Leclerc by one tenth, with team-mate Sergio Perez another tenth in arrears.
The Dutchman sounded shocked on the Red Bull team radio when his race engineer Gianpiero Lambiase informed him his lap was enough to line up first on Saturday, and afterwards he explained his car felt difficult to drive over one lap.
"To be honest with you, it felt pretty terrible," Verstappen said. "I don't know, maybe the last session was just incredibly difficult to get the tyres to work, because already in SQ2 I didn't feel great. SQ3 I think it felt quite similar for me.
"I didn't really improve a lot on the soft, but somehow we are first. I will happily take it, but it didn't really feel enjoyable out there to drive for whatever reason."
Verstappen said he had been confident he could fight for pole after Friday's single 60-minute practice session, but that confidence disappeared once he exited the garage for qualifying, while Norris topped both SQ1 and SQ2.
"In practice it felt really, really nice. I was very comfortable and confident, in qualifying not so much," he added.
"I thought after practice, I was quite confident that we could really fight for pole then in qualifying it didn't really look like that for me.
"But somehow we still ended up in first. I don't know what happened to the other cars in the last lap."
Behind Leclerc and Perez, Verstappen's former team-mate Daniel Ricciardo bounced back from a tough start to the 2024 season by grabbing fourth for RB.
