Mercedes's George Russell finished second, 4.951 seconds behind the Australian, whose win was his first of any sort since the Dutch Grand Prix at the end of August, with Norris third and Red Bull's Max Verstappen fourth.
Norris now has 396 points with Piastri on 374 and Verstappen on 371, with 50 remaining to be won.
Qualifying for the main grand prix is later today, with Norris still in a position to win his first championship on Sunday.
"I think the last couple of weekends has just been things going wrong rather than a lack of pace," Piastri said after 19 laps of the floodlit Lusail circuit.
“Here, everything’s gone smoothly so far, and the pace has been strong. It’s a track I’ve enjoyed in the past, and I’m enjoying it again, clearly."
Norris had recognised before the start that overtaking would be a problem, and he was not wrong.
“It’s going to be a tough race tomorrow... it’s not easy to pass around here, it’s too difficult, so it’s all about qualifying,” he said.
Yuki Tsunoda finished fifth for Red Bull, after obligingly moving aside for teammate Verstappen on the opening lap, with Kimi Antonelli sixth for Mercedes after a five-second penalty for a track limits violation demoted him one place.
Fernando Alonso was seventh for Aston Martin, after starting fourth, and Carlos Sainz was eighth for Williams.
Piastri's win was his first in a sprint this season, and he was never challenged or troubled from the moment the lights went out, with Russell and Norris almost touching in the race for the first corner but avoiding contact.
Verstappen complained again that the bouncing that had plagued him in qualifying was back, but he still made up two places on his starting position.