The Australian lost the front of his bike through the second part of the Turn 10 chicane. He was unhurt and able to return to the pits for his second bike, on which he then proceeded to pull clear in the final five minutes.
Repsol Honda's Stoner, who led both Friday sessions, continued his excellent form with a time of a minute 33.945 seconds.
As was the case in second practice, the reigning champion ended as the only man to dip under the 1m34s mark, giving him an advantage of almost half a second at the head of the field.
Before the weekend, the Australian announced that he would retire at the end of the season.
Until his late charge, the session had been incredibly close with the top eight riders covered by less than six tenths of a second.
Briton Cal Crutchlow eventually claimed second fastest, fractions ahead of his Tech 3 Yamaha team-mate Andrea Dovizioso.
Yamaha's Jorge Lorenzo, Gresini's Alvaro Bautista, Honda's Dani Pedrosa and Ducati's Valentino Rossi all ended within 0.4s of the Tech 3 duo.
Hector Barbera's satellite Pramac Ducati beat Nicky Hayden's works counterpart to eighth, while Karel Abraham on the Cardion Ducati beat Yamaha's Ben Spies and LCR Honda's Stefan Bradl to 10th.
Aspar's Randy de Puniet occupied his seemingly customary position as top CRT rider in 13th.
The cold conditions which contributed to Stoner's fall also caught out Ioda's Danilo Petrucci and Speed Master's Mattia Pasini early on. Pasini was able to walk away from a heavy high side, but did not return to the track.