Spaniard Espargaro, who failed to finish either of his past two races, shot to the top of the timesheets in the second session at the Red Bull Ring after Australian Jack Miller was fastest in the morning.
Espargaro was 0.221sec ahead of Ducati-Pramac rider Miller.
Italian Andrea Dovizioso, the winner of the Austrian Grand Prix for the Ducati factory team five days ago, was a close third.
Portugal’s Miguel Oliveira of the KTM team satellite outfit, KTM-Red Bull-Tech 3, was fourth on the stable’s home track, while championship leader Fabio Quartararo could only manage 14th.
Quartararo has finished seventh and eighth since winning the opening two races of the coronavirus-hit campaign.
He holds an 11-point lead over Dovizioso in the championship standings.
Frenchman Johann Zarco, penalised Friday for his role in a crash with Franco Morbidelli last week, did not take part in the session after undergoing surgery on the wrist he injured in the collision.
Zarco was sanctioned for “irresponsible riding” and will start his next race from the pitlane as punishment.
He has been cleared to ride in Saturday qualifying.
“I am not happy with the sanction,” said the 30-year-old Zarco.
“I thought about appealing but it would be complicated.
“I would rather start in the pit lane this weekend and end this story which is not funny.”
Despite split feelings in the paddock over the punishment handed out to the French rider, Morbidelli said Friday he has moved on.
“I don’t care about the incident now,” he said.
“The accident is already gone for me, from the moment I gave my opinion about the accident my chapter on this history was closed and the chapter was opened up for the stewards.”
The collision between Zarco and Morbidelli last Sunday resulted in a terrifying near-miss for nine-time world champion Valentino Rossi.
The stray bike of Morbidelli, careering through the air at around 300kmh, missed him by just centimetres.
Zarco’s machine almost took out Rossi’s Yamaha teammate Maverick Vinales.
On Friday, Vinales was eighth fastest with Rossi in 13th place.
“The bigger problem today was that we tried to do the time attack in the afternoon, but the asphalt was more than 50 degrees,” said Rossi who was fifth last week despite being left “shaken” by his near-miss.
“About my pace, we’re not so bad, but as always there are many riders who are very strong.”
Injured defending champion Marc Marquez will miss his fourth race in a row after breaking an arm. Francesco Bagnaia is also still sidelined.
Combined Styrian MotoGP first and second free practice times:
1. Pol Espargaro (ESP/KTM) 1.23:638, 2. Jack Miller (AUS/Ducati-Pramac) at 0.221sec, 3. Andrea Dovizioso (ITA/Ducati) 0.225, 4. Miguel Oliveira (POR/KTM-Tech3) 0.260, 5. Takaaki Nakagami (JPN/Honda-LCR) 0.266, 6. Joan Mir (ESP/Suzuki) 0.269, 7. Alex Rins (ESP/Suzuki) 0.371, 8. Maverick Vinales (ESP/Yamaha) 0.422, 9. Franco Morbidelli (ITA/Yamaha-SRT) 0.549, 10. Brad Binder (RSA/KTM) 0.613
13. Valentino Rossi (ITA/Yamaha) 0.720, 14. Fabio Quartararo (FRA/Yamaha-SRT) 0.743