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.
A tactical gamble by Iannone worked out well as he was the only rider to combine a soft front with a medium rear tire while nearly all others picked a medium-hard combination.
The Austrian honours went to Italy's Andrea Iannone ahead of Ducati teammate and compatriot Andrea Dovizioso, followed by the Yamaha duo of Jorge Lorenzo and Valentino Rossi.
Marquez, who took his only MotoGP victory in Brno in his rookie season in 2013, leads the overall standings on 181 points, ahead of Lorenzo with 138 and Rossi with 124. Anyway, it was a good race. Championship leader Brad Binder (KTM) crashed out of the lead with four laps to go, before Khairul Idham Pawi (Honda) also ended up in the gravel in a dramatic change for the race in the final few laps.
"But we are happy with the second place, especially because we have a good pace, good setup to keep a constant pace during the race". At the start he spoke of how everyone overtook him on the outside and then when he seen via his pit board that he was "P12" he was gutted.
"I took the gamble", said Crutchlow. Comparing the performance of the factory Yamaha to the independent team ones ridden by Monster Tech 3 Yamaha riders Pol Espargaro and Bradley Smith, he noticed that "already in half of the race they were very better".
Valentino Rossi hopes for better fortunes at the Czech Republic MotoGP this weekend after surrendering plenty of time to fellow Movistar Yamaha rider Jorge Lorenzo 12 months ago.
"We are the first, we have the fastest time but ... we must improve a lot".
"We need to stay in the fight again and try to recover some more points for the championship", he said.
The LCR Honda rider raced to the victory, the first British MotoGP victor since Barry Sheene in 1981, by 7.3 seconds over Rossi.