The Welshman battled all the way to finish five minutes behind stage victor and new race leader Nairo Quintana of Movistar but dropped to 17th overall, while Landa tumbled down the standings after finishing over 26 minutes in arrears.
The crash Sunday virtually ended the overall title hopes of Sky teammates Geraint Thomas and Mikel Landa, plus Orica-Scott's Adam Yates.
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.
Jungels fell the 12th place in the general classification, while Pinot and Dumoulin were able to stay within half a minute of Quintana. Mollema is fourth, 51 seconds behind, and Nibali is fifth, 1:10 back.
But both Sky riders saw their hopes dashed when Dutchman Wilco Kelderman clipped a police motorcycle that was parked on the left side of the road.
Thomas, who hurt his right shoulder, needed a couple of minutes to get back on his bike.
Immediately after the crash, Nairo Quintana's Movistar team set a blistering pace at the front, which prompted previous leader Bob Jungels to drop off during the early stages of the climb. Yates is one position ahead of Thomas on GC, but is now 4 minutes 49 seconds behind the Colombian.
Entering the stage, Thomas stood second overall and Yates was third.
At last year's Tour de France, organisers re-set the stage times for Australian Richie Porte, Britain's Chris Froome and Dutchman Bauke Mollema after they crashed into a motorbike on Mont Ventoux.
He said: "It's ridiculous and shouldn't happen".
And he was highly critical of race organisers when speaking to reporters following the end of a miserable day, as he said: "It's really disappointing, I don't know what to say". My shoulder popped out as well.
After a rest day Monday, the Giro resumes Tuesday with a 39.8 (25-mile) individual time trial from Foligno to Montefalco through the Sagrantino winemaking region in Umbria.