The Aprilia rider erased the time set by world championship leader Fabio Quartararo of Yamaha on Friday, relegating the Frenchman to sixth place.
Espargaro, second in the championship behind Quartararo going into the 12th round of the MotoGP season on Sunday, puts pressure on the Frenchman by taking the best time before qualifying.
The Spaniard led three Ducati riders with compatriot Jorge Martin just 0.028sec slower over the 5.9 km circuit.
Australian Jack Miller and Frenchman Johann Zarco followed less than a tenth of a second behind Espargaro.
Zarco could have done even better, but he crashed on a very fast lap.
Quartararo was 0.328sec off the pace but ensured the essential of a top ten finish with sixth best.
Top times after three rounds of free practice:
1. Aleix Espargaro (ESP/Aprilia) 1min 58.254sec, 2. Jorge Martin (ESP/Ducati-Pramac) at 0.028sec, 3. Jack Miller (AUS/Ducati) 0.078, 4. Johann Zarco (FRA/Ducati-Pramac) 0.090, 5. Maverick Vinales (ESP/Aprilia) 0.321, 6. Fabio Quartararo (FRA/Yamaha) 0.328, 7. Francesco Bagnaia (ITA/Ducati) 0.371, 8. Joan Mir (ESP/Suzuki) 0.403, 9. Luca Marini (ITA/Ducati-VR46) 0.409, 10. Alex Rins (ESP/Suzuki) 0.475