Piastri challenged Briton Norris hard in the first stint after passing Ferrari’s Charles Leclerc, which had split the McLarens in qualifying, at the first corner.
The Australian briefly took the lead at Turn Three on lap 11, only for Norris to repass at the next corner.
And Piastri flirted with disaster when he made a late dive down the inside at Turn Four on lap 20, locking up his brakes and narrowly avoiding hitting the back of Norris’ car.
Norris made his first stop at the end of that lap. Piastri waited three further laps before making his, and Norris seemed to be in control through the middle stint.
But after their final stops, which they made one after the other with 17 and 16 laps to go, Piastri began to close in again.
Coming out from his stop four seconds behind, Piastri was within two seconds of Norris with 10 laps to go, and Norris went on the radio to tell his engineer Will Joseph that he “needed some pace – please help”.
But Norris, despite some damage on his front wing, managed to stabilise the gap and hold on to the chequered flag for a much-needed victory, two weeks after he ended his own Canadian Grand Prix by running into the back of with his team-mate.