The Yamaha rider posted a new lap record of one minute 55.799 seconds as he beat Crutchlow to top spot by just 0.196 secs.
Repsol Honda's Dani Pedrosa had to be content with third place on the grid despite setting the pace in all of the practice sessions leading up to qualifying.
The Spaniard suffered a crash early in the session and afterwards never had the pace to compete with the front two.
Pedrosa trails Lorenzo by 18 points at the head of the riders' standings.
Second place for Crutchlow represents his best qualifying performance in MotoGP, and continued a good day for the Briton after it was announced he would remain with Tech 3 Yamaha next season.
"It's nice to be back in the top three," Crutchlow told BBC Sport. "Hopefully we'll make it in the race.
"I don't think we're far away. I like the track here and it suits my riding style."
Row two is headed by Lorenzo's team-mate Ben Spies, while Crutchlow's team-mate Andrea Dovizioso was fifth and Ducati's Valentino Rossi sixth.