Piastri was hindered by brake problems during the opening session, though he recovered to set the third quickest time, while world champion Norris had to spend the first 45 minutes off-track as mechanics grappled with a hydraulics problem.
He eventually emerged to finish seventh but better was to come in second practice at the sweltering Spielberg circuit on Friday.
Piastri took second behind Antonelli, a place ahead of Norris, and afterwards reflected on some lessons learned.
He said: "We had a pretty good day finishing well in both sessions. We knew Mercedes would be a step ahead, and that's how it played out, but it was productive for us.
"We worked through a lot of setup items and got through some homework carried over from Spain. We did a good job trialling different approaches and understanding the car better.
"Looking ahead to tomorrow, there are definitely areas where we can learn overnight to help close the gap, but I am feeling more comfortable, and I'm happy with how today has gone. We'll focus on incremental gains and see where that gets us."
The man to catch remains Antonelli, who rebounded from heartbreak in Barcelona by dominating Friday's sparring sessions in Austria.
He pipped team-mate George Russell by four-hundredths of a second in the opening session, then was 0.237 seconds quicker than Piastri.
Max Verstappen was in an upgraded car from home team Red Bull but appeared to have problems with his seat at the start of the second session. He was fourth fastest in both sessions.
Lewis Hamilton, who had claimed his first win in a Ferrari at the Barcelona-Catalunya race a fortnight ago, twice locked up his tyres to place fifth in his two outings.
Antonelli was stopped by a technical problem late in the Barcelona race which ended the Italian teenager's run of five straight victories.
He tops the championship 41 points ahead of Hamilton and 50 ahead of Russell.
Sergio Perez stopped on the track in his Cadillac in both first and second practice. The Mexican said the problem appeared to be same.
First practice was red flagged for a time, while his car again ground to a halt early in the second session when a virtual safety car phase ensued.
Saturday qualifying is expected to be even hotter, with Europe's heatwave possibly intensifying for Sunday's race.
