Verstappen on top in Austria after Norris runs off in practice
The 26-year-old Dutchman clocked his best time of one minute 5.685 seconds to outpace Piastri by 0.276sec with Ferrari's Charles Leclerc third, ahead of team-mate Carlos Sainz and seven-time champion Lewis Hamilton of Mercedes.
Ferrari-bound Hamilton and team-mate George Russell ran throughout on hard tyres and did not take softs for a late dash for a fast lap time unlike all the others in the top 10.
Esteban Ocon, who leaves Alpine at the end of the season, was sixth ahead of Aston Martin's Lance Stroll, Russell, Yuki Tsunoda of RB and two-time champion Fernando Alonso in the second Aston Martin.
Lando Norris, in the second McLaren, lost control of his car on his flying late lap and wound up 13th behind Pierre Gasly of Alpine and the struggling Sergio Perez, in the second Red Bull.
On a warm day in the Styrian Alps, with rain threatening, Verstappen was the first out of the pits as the session began, followed by the two Mercedes, both running on hard tyres on which they quickly established an impressive one-two at the top of the times.
Perez also demonstrated a glimpse of a possible return to form by taking fourth while Yuki Tsunoda ran off track at Turn One and reported his steering column felt "weird", although his request to change it was rebuffed.
Verstappen's progress came to a halt after 31 minutes of the hour when he lost power and came to a halt in his Red Bull on the main straight.
"Engine fault," he reported to the team as his car, with the help of marshals, was reversed back to a gap in the pit-wall and the pits.
If he had reversed deliberately, Verstappen risked a visit to the stewards' office for an infringement of the regulations.
After a five-minute, red-flagged pause, the action resumed with Verstappen joining the fray immediately, as if nothing had happened.
A rapid re-boot seemed to have worked wonders and solved what was described later as a 'sensor' issue.
The drivers return to the track at 1415 for qualifying for Saturday's sprint.