The Spaniard, following up his win in Spain last time out, made light of the tricky early wet conditions to cross the line five seconds clear of Crutchlow.
The Briton manfully shrugged off a fracture to his right shin in a crash in qualifying 24 hours earlier to notch up his best ever MotoGP result.
In third came pole-sitter Marc Marquez, who struggled for grip on the slippery Bugatti circuit in the early stages before fighting back strongly.
Pedrosa now leads the overall standings on 83 points with MotoGP rookie Marquez second on 77 points and defending champion Jorge Lorenzo eleven points adrift in third.
“It was a very good race for me,” said Pedrosa after his first MotoGP win at the Le Mans circuit. “I’m so happy with this one because I lost some position sliding at the start but recovered at the first turn. I had no grip on the rear.
I then started to have some good feeling in the wet, so I tried to push but made a couple of mistakes and almost went off twice.” At the off Marquez slipped down the field to eighth with the pack led by Andrea Dovizioso, Lorenzo and Pedrosa.
Pedrosa took control with 23 laps remaining as Valentino Rossi, targeting his 80th MotoGP win, crept up to lie fourth from eighth on the grid. With the track drying as the sun came out Lorenzo surprisingly dropped off the pace as Pedrosa and Dovizioso continued their battle for superiority.
Rossi suffered misfortune on lap 11 when he lost control of his Yamaha, his bike slithering unceremoniously into the safety gravel rounding a turn while vying for fourth place with Nicky Hayden.
The Italian dusted himself off and climbed back on board to resume in 12th. Pedrosa, meanwhile, had put plenty of daylight between himself and the chasing pack, keeping out of trouble in the closing stages to coast home alone.