"It’s the best day of my racing career," said the 30-year-old rider, who became a father for the first time three weeks ago. He was joined on the podium by Yamaha's Italian Valentino Rossi and Honda's championship leader Marc Marquez.
"We worked hard for this and I took the gamble.
"Not many other people did and as far as I’m concerned they’re all wimps," added Crutchlow, who had started in 10th position on the grid and was 15th at the end of the opening lap before taking the lead with seven to go.
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Crutchlow, who beat Rossi by 7.298 seconds, was one of only two riders who chose a hard option tyre for front and rear in a decision that paid off in the conditions as those on softer compounds paid the price.
The victory was also a first for his LCR team.
Torrential rain fell before the race but stopped ahead of the start, leaving riders a tough choice to make on tyres with some opting for softs in the expectation that a bike change would be needed.
Spain's world champion Jorge Lorenzo, Rossi's team mate, made two changes -- once to slick tyres and then back again -- and finished 17th.
Marquez has 197 points after 11 of 18 races with Rossi on 144 and Lorenzo on 138. Crutchlow's home British Grand Prix at Silverstone is next up on Sept. 4.
(Reporting by Alan Baldwin, editing by Brian Homewood)
