Miller clocked a best time of one minute 37.709 seconds on a KTM, setting a new lap record at the Portimao circuit.
Maverick Vinales, of Aprilia, and reigning world champion Francesco Bagnaia, on a Ducati, filled out the top three.
However, the high-speed crash suffered by 31-year-old Espargaro on his KTM Tech3 GASGAS bike caused a long interruption to the session which eventually finished around two hours late.
The Spaniard, who moved to his new team after two disappointing seasons at Honda, lost control of his machine on Turn 10 in the second session and was catapulted off the track.
Espargaro, who rolled into a wall, was treated trackside for around half an hour before being airlifted to hospital by helicopter to Faro for treatment to a back and neck injury.
"He suffered a dorsal and thoracic trauma," said a statement from championship promoter Dorna.
Espargaro was "conscious" at the time "and was transferred to Faro hospital for further examinations."
A crash in the dying minutes of the session for six-time MotoGP world champion Marc Marquez on a factory Honda meant the Spaniard, who has undergone four surgeries in recent seasons, was out of the Top 10.
He will have to fight through the first qualifying session for a chance of a spot in the second run on Saturday.
Earlier, the session had also been delayed by technical issues which affected the timing mechanism.
The top 10 in practice on Friday was completed by Luca Marini, Jorge Martin, Fabio Quartararo, Johann Zarco, Marco Bezzecchi, Aleix Espargaro and Enea Bastiaini.
