Crutchlow, celebrating a third career MotoGP win and Honda's 750th grand prix success, is the first Briton to lead the top category since the late Barry Sheene in 1979.
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In a thrilling race during which Honda's reigning world champion Marc Marquez was penalised for a collision with Yamaha's Italian great Valentino Rossi, Frenchman Johann Zarco finished a close second for Tech3 Yamaha.
Image credit: Eurosport
Spaniard Alex Rins was third for Suzuki at the Termas de Rio Hondo circuit.
Crutchlow now has 38 points, three more than Ducati's Italian Andrea Dovizioso.
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