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Norris headed the field though had a near miss as the chequered flag fell with Isack Hadjar, from Lance Stroll in second.
Piastri was third despite problems which saw his session end five minutes early, while Daniel Ricciardo was 13th and Jack Doohan 17th.
It was a busy start to the session, McLaren sending Norris out with a significant aero rake fitted to his car.
He had an older-spec front wing on the car, versus the newer model fitted to Piastri’s car.
Stroll was among those out early, though he was soon back in the garage as he complained of a brake-by-wire issue in his Aston Martin.
Alongside the regular drivers, a quartet of juniors were completing Free Practice 1 sessions; Oliver Bearman at Haas (Kevin Magnussen), Doohan for Alpine (Pierre Gasly), Franco Colapinto for Williams (Logan Sargeant), and Hadjar for Red Bull Racing (Sergio Perez).
A red flag halted proceedings after nine minutes, triggered by Yuki Tsunoda who spun at Luffield and beached it in the gravel trap.
He’d managed five laps to that point, with a best of 1:29.864s, around a second back from the benchmark time set by George Russell with a 1:28.888s.
Eight minutes after the session was halted, it resumed.
Third fastest under the stoppage, Max Verstappen headed out on a set of hard compound tyres, the rear wing of his Red Bull Racing coated in flo vis paint.
He improved to second fastest with a 1:28.370s, Russell having improved to 1:28.156s.
Just before the halfway point, Carlos Sainz moved to the top of the timesheets for Ferrari.
The Spaniard logged a 1:27.925s on a set of hard compound tyres, to head Lewis Hamilton by 0.118s who’d also pipped his team-mate to sit second fastest.
Doohan logged 10 laps through the first 30 minutes as he sat 18th fastest, his best a 1:30.110s in the Alpine.
There was a problem with his car, however, which temporarily delayed his running.
Soon after, Verstappen moved to the top of the timesheets with a 1:27.764s, the Dutchman not outright fastest in any of the three sectors.
Russell was second fastest from Charles Leclerc, making for three different teams in the top three places.
On a new set of soft tyres, Piastri went fastest with a 1:27.631s, an improvement of 0.098s.
The Australian’s lap signalled the start of soft tyre running, Norris going fourth fastest with a 1:27.836s.
On his soft tyre run, Doohan encountered traffic in the final complex that forced him to abort a lap, though he’d by that time logged a 1:28.735s to sit 16th fastest.
A second run for Norris saw the McLaren driver shoot to the top of the timesheets, with Stroll slotting in second best.
With 10 minutes remaining, Russell reported back that it was starting to drizzle.
Mercedes had not followed the crowd as the Austrian Grand Prix winner remained on medium rubber.
At McLaren, Piastri reported a suspected hydraulic problem in his car, rolling the MCL38 into pit lane.
He didn’t quite make it, stopping in the pit entry which was closed as officials pushed his car clear.
With less than four minutes remaining by the time the team recovered his car, Piastri’s session was over.
The order didn’t change to the chequered flag, Norris ending it fastest from Stroll and Piastri.
Verstappen was then fourth best ahead of Russell, while Daniel Ricciardo was anonymous en route to 13th in the session.
Doohan slipped to 17th at the end, logging 22 laps in his hour of running.
The 21-year-old’s running is now complete, with Gasly set to climb back aboard the car for the remainder of the weekend.
There was a late scare for Norris, who encountered Hadjar through Abbey who was dawdling on the racing line.
The rookie had no warning the McLaren was approaching, a near miss officials will investigate ahead of Free Practice 2.
That follows at 16:00 local time (01:00 AEST).
