Crutchlow set the quickest time of the weekend so far - his best lap a 1:38.975s - to become the first driver to dip below the 1:39s mark.
His satellite Tech 3 Yamaha, which had experienced a front-brake problem earlier in the session, edged out Dani Pedrosa's Honda by less than two hundredths of a second.
Friday pacesetter Jorge Lorenzo was third fastest, the 26-year-old starting his birthday by beating Yamaha team-mate Valentino Rossi to fourth.
Marc Marquez was only sixth on the timesheets, well behind the leading four, who have been clear of the rest in all three sessions. He was beaten by Andrea Dovizioso, who gave Ducati some encouragement by completing the top five.
Marquez was only a tenth ahead of the lead CRT bike - Hector Barbera's Avintia FTR, the pace of which was such that he demoted Nicky Hayden in the second Ducati, Andrea Iannone's Pramac Ducati and Alvaro Bautista's Gresini Honda.
Stefan Bradl will have to fight for his place in second qualifying after the LCR Honda missed out on the top ten altogether, a combination of traffic and an error on his final flier condemning him to 11th.
Karel Abraham did not feature in third practice. The Czech rider broke his collarbone two weeks ago in Austin and withdrew after taking part in Friday practice.
- Sports & Recreation
- Dani Pedrosa
- Marc Marquez
- Valentino Rossi