Team Sky's Geraint Thomas and Orica-Scott's Adam Yates were both brought down in a crash at the foot of the climb when a stationary police motorbike at the side of the road caused a big pile-up.
Thomas, who hurt his right shoulder, needed a couple of minutes to get back on his bike.
Yates finished four minutes 38 seconds behind and Thomas's ordeal ended 5:07 after Quintana had crossed the line.
"I've had worse crashes," said Thomas. "My shoulder is sore but it's nothing I can't deal with. There's a lot more racing to be had so we'll get stuck in."
"These things happen in sport," said Team Sky principal Dave Brailsford. "You’ve just got to stay calm and not over-react. Obviously there’s emotion but my role here is to keep the guys calm, assess the situation and look at how we go on from here."
Colombian Quintana (Movistar), looking to win his second Giro title, made the decisive move 4.7 km from the finish line of the 149-km ninth stage from Montenero de Bisaccia, dropping Frenchman Thibaut Pinot (FDJ) and Nibali (Bahrain-Merida).
Pinot limited the damage to take second place, finishing just ahead of Dutchman Tom Dumoulin (Team Sunweb), 24 seconds off the pace.
Nibali was fifth, 59 seconds behind Quintana.
Overall, Quintana leads second-placed Pinot by 28 seconds and third-placed Dumoulin by 30 seconds.
Another Dutchman, Bauke Mollema (Trek-Segafredo), who was fourth on the day, is fourth overall 51 seconds off the pace and fifth-placed Nibali is 1:10 behind Quintana.
Monday is a rest day and Tuesday's 10th stage is a 39.8-km individual time trial that should see Dumoulin, originally a time-trial specialist, gain time on his rivals.
(Reporting by Julien Pretot; Editing by Toby Davis and Clare Fallon)
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