Movistar rider Dowsett had a three-hour wait before all the favourites had finished and he could be sure of victory in the 54-kilometre technical time trial, with Wiggins second at 10 seconds, Estonian Tanel Kangert third at 14 seconds, and Italy's Nibali fourth at 21 seconds.
Following the Giro's first key battle for the overall classification, 2010 Vuelta a Espana winner Nibali captured his first lead in the Giro since 2010, with Australia's Cadel Evans second at 29 seconds, Dutchman Robert Gesink third at 1 minute and 15 seconds, and Wiggins fourth at 1 minute and 16 seconds.
"It's a surprise to take the pink jersey (of race leader) so early but I'm very pleased to have it," Nibali, who rides for the Kazakh Astana squad, told reporters.
"But I'm not taking anything for granted. I'm sure that Gesink, Evans, Wiggins and (Michele) Scarponi (of Italy, 2011 race winner) will fight until the end.
"We can't rule out (Ryder) Hesjedal (of Canada) either. There's a long way to go yet and I'm sure the third week will see a lot of battles in the high mountains."
A minute ahead of Wiggins at the first checkpoint after the Briton had a slow puncture and bike change, Nibali trailed the Sky rider by 11 seconds at the finish as Wiggins fought back on the second part of the course.
"The first part of the race has been difficult in general, not just the time trial," Nibali said, "and I know I will have to grab seconds wherever I can in the days to come."
2012 Tour de France winner Wiggins rose from 23rd to fourth overall, but fell 10 seconds short of taking a morale-boosting stage win after a first week plagued with crashes, delays and unexpected time losses.
"I think that puncture broke his rhythm," Sky's performance manager Rod Ellingworth told reporters.
"He hit something on the road and it was two or two and a half kilometres before he realised he' done something to the bike."
A frustrated Wiggins uttered one word to the press - "Yes" - when asked if he thought he had lost the time trial because of the puncture.
Last year's Giro d'Italia winner Hesjedal finished 18th on the stage and dropped to sixth overall.
Dowsett clinched his first stage win and said: "The wait was horrible. It went on for so long. When you're out on the bike at least you can get everything out, and I kept on overtaking riders. But it was a long time sitting there before I knew I'd won."
The Giro d'Italia finishes on May 26 in Brescia.
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