Norris had it all to do after locking his front brakes going into the first corner on his first run in the shootout.
Piastri crashed out of third place in the sprint earlier in the day to fall nine points behind Norris in the championship but he nailed his first lap to go fastest from Leclerc.
But Norris has looked the man to beat all weekend and he delivered an impressive lap on his final run, under intense pressure, to beat his team-mate by 0.375secs.
“I felt good. I was under a bit of pressure because I locked up on my first lap so a little bit more stressful than I would have liked but stayed cool and very happy,” said Norris.
“Locking up into Turn One puts unnecessary pressure on myself but when I’m in a good rhythm, when I can out it all together, I’ll be on top.”,
Piastri said: “Obviously, bit disappointed with the result but the car has looked quick this weekend, especially over a longer run, so hopefully I can take advantage of that tomorrow.
“Ultimately, I’ll try and take whatever opportunities arise and if I can make progress forward and put pressure on, I will. But yeah, got to get there first.
Antonelli, who pushed Norris all the way in the sprint, has been the lead Mercedes driver all weekend.
“I am a bit annoyed I am again behind him,” the 19-year-old said. “We were so close again behind him, very tough to put the lap together with the wind. But managed to put a decant lap on the final run and happy with that.”
