Australian Piastri, the winner of the last race in China, squeezed in a lap of 01: 28.114 seconds between the last two red flags to take the honours on a sunny but cool day at the Suzuka circuit.
Championship leader Norris was fastest in first practice and second in the later session, some fourth tenths of a second ahead of Racing Bulls' French rookie Isack Hadjar.
The level of disruption in the second session meant several drivers were unable to get out for extended runs, leaving plenty for them and their teams to figure out in the final practice before qualifying on Saturday.
The second session was little more than seven minutes old when Jack Doohan's Alpine spun off the track at the first corner, skidded across the gravel and slammed into a wall.
The Australian rookie, who had been replaced by reserve driver Ryo Hirakawa for first practice, looked shaken as he was helped to walk away from the wreckage of his car.
However, his team confirmed afterwards that he was okay to complete the rest of the weekend.
The cars were kept off the track for 22 minutes and had returned for only three minutes when the session was red-flagged again after Spaniard Fernando Alonso came off the track and got his Aston Martin stuck in the gravel.
A seven-minute stoppage was followed by five minutes of action before a patch of grass at the trackside caught fire, bringing the red flags out yet again.
Piastri got his flying lap in to pip Norris to the top of the timesheets before another patch of grass, perhaps ignited by sparks from a passing car, went up in flames to bring a premature end to the session.
It was a disappointing session for the crowd, who had earlier cheered Japan's Yuki Tsunoda to the sixth-fastest time in the opening session for Red Bull after he was promoted from the Racing Bulls team at the expense of Liam Lawson; he was just a tenth slower than teammate Max Verstappen.
Dutchman Verstappen complained about understeer in the second session, finishing more than half a second off the pace with the eighth-fastest time, while Tsunoda was down in 18th.
New Zealander Lawson, back at the Racing Bulls team, was only able to manage the 13th fastest time in the opening session but was fifth in the second.