Mexican Perez needed to finish in the top three to keep the title race open for another day, with the main grand prix on Sunday, but his hopes ended in a cloud of dust after tangling with Alpine’s Esteban Ocon and Haas’s Nico Hulkenberg on lap 11.
The Red Bull car was then stuck in the gravel, with Perez stepping out.
That meant Verstappen, who started third and finished second behind McLaren’s Oscar Piastri, became champion for the third year in a row with an unassailable lead of 184 points and only 172 left to win.
Team boss Christian Horner read out a roll call of greats over the radio after the 26-year-old Dutch driver crossed the finish line.
“Max, you are a three-time world champion. That’s unbelievable. It’s been an incredible year for you,” said Horner.
Verstappen, who has won 13 of the 16 grand prix so far, including 10 in a row, replied, “Yeah, unbelievable guys. I don’t know what to say. Thank you for providing me with such a car. It’s been a lot of fun this year.”
He also became the second-youngest three-time world champion after now-retired German Sebastian Vettel, who secured the third of his four crowns with Red Bull in 2012 at the age of 25, and the first to win the title in a sprint event.
The last to take the title on a Saturday was Brazilian triple-champion Nelson Piquet in the 1980s.
Piastri’s success ended Red Bull’s domination of the sprints this season and earned the Australian rookie his first victory in F1, even if it was not a proper grand prix for the record books.
“When he (Verstappen) got through to second I thought I was going to be in a bit of trouble, but the pace was good. First sprint win sounds pretty cool,” said Piastri, who finished 1.871s ahead.
His teammate Lando Norris finished third with Mercedes’ George Russell fourth, and teammate Lewis Hamilton fifth after starting 12th and taking advantage of the collisions ahead of him.
Ferrari’s Carlos Sainz was sixth with teammate Charles Leclerc seventh at the flag. However, Leclerc was later handed a five-second penalty for exceeding track limits, which demoted him out of the points.
That moved Williams’ Alex Albon up to seventh with Fernando Alonso eighth for Aston Martin.
While Piastri led away into the first corner on medium tyres, and Russell using his softs to slot into second, Verstappen on mediums dropped initially to fifth, and Perez to 11th.
That all but ended the contest, with Perez making no progress through the field.
Those on the mediums had the last laugh, however, as the softs wore down and Piastri passed Russell to take back the lead on lap 11.
The safety car was kept busy throughout, deployed shortly after the start when AlphaTauri’s Liam Lawson went off at turn two and his car became stuck in the gravel.
The incident came at the end of lap two, which gave Russell enough time to take the lead, before Logan Sargeant also spun his Williams into the gravel a lap later, triggering another safety car deployment.
The safety car then came out a third time to deal with Perez’s accident, leaving five laps of racing at the end and not enough time for Verstappen to catch Piastri.
The Dutch driver will start Sunday’s main grand prix at Lusail in pole position.