McLaren's British driver Lando Norris races during the Sprint race at the Jose Carlos Pace racetrack, aka Interlagos, in Sao Paulo, Brazil. AFP
The title-chasing Briton took the lead on lap 22 of the 24-lap race, when Piastri swapped positions with him before fending off the challenge of three-time champion Verstappen in his Red Bull.
Norris, 24, came home 0.593 seconds clear of Piastri who finished 1.5 seconds ahead of the Dutchman with Charles Leclerc finishing fourth.
Norris admitted he was fortunate to collect his first career sprint race win.
"I'm not proud of it, but it worked well and as a team we had a good day -– and thanks to Oscar," said Norris.
"He deserved to win, but it was good team work and we had great pace. And we executed it well."
Verstappen leads Norris by 45 points with four races including Sunday's to come -- and one sprint -- and it could get worse for the Dutch driver.
At the finish Verstappen -- who will start with a five-place grid penalty -- was noted for an infringement of the Virtual Safety Car (VSC) rules.
"It was a tricky race," said Verstappen.
"The pace was good and I'm quite pleased with that although it took quite a long time for me to pass Charles (Leclerc) -- I had to wait for a mistake to pass him."
He added he would be aiming to 'limit the damage' to his title defence in Sunday's race.
McLaren's one-two success lifted them 35 points clear of Ferrari in the constructors' championship and ended Verstappen's run of four consecutive sprint wins this year.
Red Bull Racing's Dutch driver Max Verstappen (L) speaks with McLaren's British driver Lando Norris after the Sprint race at the Jose Carlos Pace racetrack, aka Interlagos, in Sao Paulo, Brazil. AFP
'Dirty air'
Piastri said it had been a terrific day for the team.
"It was tricky and very bumpy out there and the racing line is very narrow, but it was a great day for the team to score a lot of points," said the Australian.
"We showed we are in decent shape."
George Russell came home sixth for Mercedes ahead of Alpine's Pierre Gasly and Sergio Perez in the second Red Bull, who collected the final point in eighth.
The race began in hot conditions with an air temperature of 28 degrees Celsius and the track at 47, making it tough on tyres.
The two McLarens made a clean start, Piastri covering off the threat of Norris while Leclerc resisted Verstappen's early attack for third at the Senna S.
Norris was clearly unhappy to be running a second adrift of his McLaren team-mate, asking his team to request Piastri to move aside, but without avail until lap 10 when he was asked to 'give Lando DRS' – a signal to switch places.
But Norris remained stuck in second in Piastri's 'dirty air' as he attempted to make his move, the top four staying in place at half distance in the 24-lap sprint.
By lap 17, tyre-wear was affecting several cars and Norris remained six-tenths adrift.
The team told him "We're happy to make the switch on the last lap," shortly before Verstappen, with Drag Reduction System (DRS) and superior pace, swept past Leclerc on the straight.
McLaren finally made their swap on lap 22, leaving Piastri vulnerable in second to the charging Verstappen before a VSC was deployed with two laps to go.
Verstappen, who closed very near to Piastri, immediately complained that he was running too slowly before the race went 'green' again for a final flying lap.
Qualifying for the Grand Prix was scheduled to take place later on Saturday amid fears of rain.
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