Norris secured his pole with his first lap in the final session, on which he was 0.189secs quicker than Piastri.
The Briton was not able to improve on his second run, which Piastri was, but a mistake at Stavelot for the Australian cost him the chance to take pole for the second day running after his sprint pole on Friday.
Norris had been nearly 0.5secs slower than Piastri in Friday’s session but he said the margin was not reflective of his true pace.
Norris said: “I was confident after yesterday – 0.3secs is just slipstream and not being first out of the pit lane. It was a decent lap, so I’m happy.”
Piastri said: “A bit disappointing. The second lap was coming together really well but just made a little mistake into 14 and lost a lot of time. The car was really good but it’s fine margins out there.
“We’re a good team-mate pairing, we learn a lot from each other. Felt like I did OK but didn’t quite execute when it matters.”
Norris now faces the same problem Piastri had in the sprint – giving the driver behind him the slipstream on the run up to the Les Combes chicane on the first lap.
Losing out to Verstappen in that way in the sprint race cost Piastri that win. Now Norris will have to defend from his championship rival.
But rain is expected for Sunday, which changes the picture because of the visibility issues of following another car in the wet.
“Most likely some rain and drizzle,” Norris said. “Could be in for a chaotic race. Going off the front and hopefully can take advantage of that and go from there.”
Verstappen had been third fastest after the first runs, but a wheelspin moment out of the La Source hairpin cost him time all the way along the straight through Eau Rouge and up to Les Combes.
The four-time champion was able to claw some of the time lost back over the rest of the lap and did improve his time slightly.
But he said the lap was “so bad” and it was enough to allow Leclerc, who felt he was able to maximise the Ferrari, to slip ahead.
He said the team had changed the car’s set-up with a view to the rain expected on Sunday but “somehow the balance didn’t really improve with that change, which is a bit weird”.
“In Q3 the first set felt awful and the second set we tried something else and it just didn’t give me any grip starting the lap,” Verstappen added.
“I already had a lot of wheel spin starting the lap out of the last corner and exactly the same happened out of Turn One and I lost 0.2secs on try lap time already.
“We tried to catch up a bit of lap time and without that problem in Turn One you look quite OK. You are quite close to the McLarens but overall it has not been a great qualifying.”
A disappointed Hamilton said to go out in Q1 was “not acceptable” but he would try to “have fun” in the race.
Behind Tsunoda, the top 10 was completed by the Racing Bulls drivers Isack Hadjar and Liam Lawson, and Sauber’s Gabriel Bortoleto, who made it into the top 10 for a grand prix qualifying session for the first time in his career, repeating the feat he managed in sprint qualifying the day before.
After progress following upgrades in the last few races, the Aston Martin drivers Fernando Alonso and Lance Stroll had a difficult day, and will line up together on the last row of the grid.
“It hurts for sure,” Alonso said. “A little bit disappointed the weekend has not been the most competitive for us. It is something on this layout which is a little worse for our package.”