As the gradients grew over 10 per cent Quintana pushed for home and the pink jersey, the Movistar rider opening up a 28-second lead over Pinot, with Tom Dumoulin third after finishing strongly.
Quintana dedicated his victory to 2011 Giro champion Michele Scarponi, who died after a collision with a van while training last month.
"The motorbike shouldn't have been there, frankly, I think we all see that", said Team Sky principal Sir Dave Brailsford after the stage. Amoung the fallen riders were both of Sky's GC hopefuls in Mikel Landa and Geraint Thomas.
Thomas said: "It's ridiculous".
Bauke Mollema (Trek-Segafredo) is 51 seconds behind in fourth and Nibali is fifth, 1min 10secs behind.
Thomas, who needed a couple of minutes to get back on his bike, appeared to be suffering from a shoulder injury. "That's the most important for now".
Quintana, who won the 2014 Giro, went on to ride away from his main rivals up the final climb and finished nicely clear of Pinot, who edged out Dumoulin in a sprint for second.
Despite the crash, Quintana put in a dominant display.
Nairo Quintana became the second Colombian this year to lead the Giro d'Italia after an impressive victory in the 9th stage.
The Welsh rider was second in the standings at the start of the stage but went on to finish over five minutes behind the leader.
Entering the stage, Thomas stood second overall and Yates was third.
Welshman Thomas stayed down for several minutes before being able to continue and later revealed his shoulder had "popped out".
Given their deficits they could abandon the race, but should they return to the road it will be for an individual time trial from Foligno to Montefalco, a route only 39.8km in length.
Thomas and Yates will have a rest day on Monday to consider their options, the British duo getting much-needed time to rest their tired and battered limbs ahead of stage 10 on Tuesday. Then there is another mountainous stage Wednesday before the Alps next weekend.
On the race's 100th edition, Giro organisers were feeling less charitable - although the general feeling in the peloton Sunday was one of anger.
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