Yet, sustaining a high pace, he caught the Movistar leader and attacked in the last 300 metres to beat Russian Ilnur Zakarin (Katusha) by three seconds and Spain's Mikel Landa by nine while Quintana ended up fourth 14 seconds behind.
Overall, Dumoulin now leads Quintana by two minutes 47 seconds and France's Thibaut Pinot (FDJ), who was fifth 35 sec off the pace on Saturday, by 3:25.
Dumoulin, a time trial specialist with decent climbing abilities, was expected to lose time on his biggest rivals in the last ascent but he managed his effort perfectly to increase his lead.
"When Quintana attacked I did not panic, I paced myself and then I gave everything I had," he said.
Quintana's original attack split the group of favourites and Dutchman Bauke Mollema (Trek Segafredo), who started the day in third place overall, cracked, losing almost two minutes as he slipped to fifth.
Defending champion Vincenzo Nibali (Bahrain-Merida) followed closely with Zakarin, Landa and Dumoulin, but when the Dutchman upped the tempo, the Italian was dropped and eventually leapfrogged by Pinot in the final kilometre.
Nibali is fourth, 3:40 behind Dumoulin, who will face his biggest test in Tuesday's 16th stage featuring a series of three daunting ascents which should favour the pure climbers.
Dumoulin has never reached the podium of a grand tour although he came close in the 2015 Tour of Spain, ending up sixth after losing the leader's jersey in the penultimate stage.
(Reporting by Julien Pretot; Editing by Ian Chadband)
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