Yamaha's Crutchlow topped the timesheets in a frantic qualifying session, moving from fourth to first on his final lap, pipping Honda's Marc Marquez by 0.357s.
Marquez had broken a finger and a toe earlier on Friday after a crash in FP3.
CR Honda's Stefan Bradl was third, with Valentino Rossi, Dani Pedrosa and Bradley Smith in row two.
With Jorge Lorenzo expected to be ruled out after breaking his collarbone on Thursday, this represents a huge opportunity for the Briton to claim a maiden MotoGP win.
However, hours after undergoing surgery in Barcelona, Lorenzo was cleared to fly back to the Netherlands and may yet try to start Saturday's race.
Crutchlow, 27, seemed unaware of the possibility of Lorenzo's return after sealing his maiden pole.
"It's good. I'm pleased obviously, but for me it's not a true pole because Jorge [Lorenzo] wasn't not here," said Crutchlow.
"I would have liked to have a dogfight with him, hopefully we'll be able to do that when he returns and hopefully for a race win later in the season.
"But we did a good job. I wasn't happy in free practice four, but if we can make the bike calmer we can go faster again. I'm looking forward to the race. We'll see what we can do."
Earlier world championship leader Dani Pedrosa fell and missed the second half of the session. He had been on provisional pole.
Honda's Pedrosa went into qualifying as pole favourite. Pedrosa duly hit the front on his first traffic-free lap and then started extending his provisional pole advantage, only to crash halfway round the lap.
Although Pedrosa was unhurt and got back to the pits, he chose not to go out on his spare bike and was left watching as he was pushed down to fifth.
Rossi was first to knock Pedrosa off the top spot, though the Yamaha legend only held provisional pole for fractions of a second before Bradl deposed him.
But Bradl would not keep hold of what would have been his first MotoGP career pole, as Marquez and Crutchlow were still on fast lap.
Marquez crossed the line first and beat Bradl by a tenth, only for Crutchlow to leave them all standing with a 1m34.398s on the Tech 3 Yamaha.
Marquez had to settle for second, followed by Bradl, Rossi and Pedrosa.
Crutchlow's team-mate Smith shrugged off his recent hand and arm surgery to take sixth.
Aspar CRT duo Aleix Espargaro and Randy de Puniet both reached Q2 and took seventh and ninth, sandwiching Alvaro Bautista's Gresini Honda.
It was a painful session for Ducati. Nicky Hayden had to battle hard to get through Q1, where he was second to de Puniet, and his team-mate Andrea Dovizioso did not make it at all.
The Italian will start way back in 15th, having been involved in an on-track spat with Hector Barbera.
Andrea Iannone was the other prototype rider to go out in Q1 when he crashed his Pramac Ducati.
Lorenzo has secured 12th on the grid as he had got into Q2 with his Thursday morning practice time.
The world champion is flying back to Assen following overnight surgery on his fractured collarbone, but will need to get medical clearance if he is to race. Yamaha has yet to confirm Lorenzo's intentions.
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- Dani Pedrosa
- Stefan Bradl
- Jorge Lorenzo
- Marc Marquez
- Valentino Rossi