Verstappen qualified first on the grid by 0.054 of a second ahead of Ferrari's Charles Leclerc, with British veteran Lewis Hamilton third and F1 Championship leader Kimi Antonelli fourth.
Besides Verstappen, the day's other big winner was Antonelli, who widened his lead over George Russell when his Mercedes teammate crashed out from the lead in the sprint.
Piastri's McLaren teammate Lando Norris was fifth but they will be next to each other on row three in Sunday's Grand Prix because of a penalty for Briton Russell.
The two collided in the last lap of the sprint race fighting for fourth place, with Norris limping home in eighth and Piastri not finishing.
World champion Norris apologised to his McLaren team after the knock which saw him attempt an overtake but clipped the Australian's rear tyre sending both cars spinning and handing Antonelli fourth place.
"Sorry about that. Obviously I didn't want that to happen but I thought I was fully alongside. I just ran out of space at the apex but I was there," Norris said over the team radio.
While Norris limped home to eighth place to claim the final point available, Piastri was forced to retire as he became one of nine cars that did not finish - a record number of retirements for a Formula One sprint race.
Piastri said he had not seen the incident but downplayed its significance as they were not in high points scoring positions.
"From where I sit, it's for fourth and fifth for a sprint race, so I'm not that bothered either way," Piastri said.
"Just obviously it's a lot of work now for the team to get both cars fixed (ahead of qualifying for Sunday's race). Just a shame for the team."
Both McLaren drivers were summoned to meet the stewards after the collision but no further action was taken.
McLaren team principal Andrea Stella was not impressed with his drivers, however, adding that scoring just one point was not enough.
"Seeing two McLarens making contact like that is simply not acceptable. This is something that we will discuss with our drivers," he said.
"We will do it in private. We will reiterate that the team interest is far bigger than any of us. There's no ego, there's no person that is bigger than the interest of the McLaren Formula One team."
Russell beat Verstappen off the line at the start in wet conditions but lost control when he put a wheel on a painted line at the end of the first lap, spinning across the track and into the barrier.
Antonelli was fourth, extending his lead over Russell from 84 points to 89, after he picked up two positions on the last lap when Norris and Piastri collided ahead of him.
Russell has a grid penalty for Sunday's Grand Prix, meaning the 20-year-old Antonelli could take another big step toward becoming F1's youngest-ever champion.
Antonelli was fourth, extending his lead over Russell from 84 points to 89, after he picked up two positions on the last lap when Norris and Piastri collided ahead of him.
Russell has a grid penalty for Sunday's Grand Prix, meaning the 20-year-old Antonelli could take another big step toward becoming F1's youngest-ever champion.
Russell wasn't the only driver to be caught out in the wet conditions. He was one of eight non-finishers after a spate of collisions and technical problems, with Red Bull's Isack Hadjar stopped by car trouble.
