After an early Verstappen error, the championship leader was running in third, between two Silver Arrows.
Lewis Hamilton led, with Bottas back in third, but Mercedes team principal Wolff explained the Finn had issues with his tyres that meant he had to head for the pit lane.
That call prompted Verstappen to pit next and he enjoyed an out lap described by Wolff as "phenomenal" while Hamilton followed him in and narrowly lost the lead.
Red Bull took a further risk by bringing Verstappen in a second time to attack the Mercedes pair on fresh medium tyres, but the first stop proved pivotal, accommodating that bold two-stop strategy.
Verstappen won the race, with runner-up Hamilton a fraction under three seconds behind him.
Wolff pondered if Mercedes had "misjudged" the undercut and added it was "something to improve".
However, he told Sky Sports: "We knew we were going to trigger the stops too early, but we had no choice."
Wolff said: "It went back and forward. We were in the lead because Max made the mistake, so that was a bit inherited.
"Then our pace was good, probably a little bit of a margin even. But then we had just about three seconds gap for the undercut, to protect the undercut, but it wasn't enough.
"We were lacking a second. Somewhere we lost it."
Red Bull boss Christian Horner added: "I think it's been a great race. You can see how close it is.
"It's been a great win for us today, but you've only got to look how tight it is between the two teams. It's going to be nip and tuck all the way through this championship, but we're going to be very happy leaving here.
"I think I'm visibly ageing with each grand prix, but we'll give Toto a few grey hairs by the end of the year as well."