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BMC's Phinney, 21, finished nine seconds ahead of another former individual pursuit specialist, Britain's Geraint Thomas, with Dane Alex Rasmussen in third a further four seconds adrift.
On what is his maiden participation in the three-week race, Phinney becomes the first American to wear the pink jersey since Christian Vande Velde, who took the race lead after winning the opening stage in Palermo in 2008.
Phinney, who signed as a professional last year for the team of reigning Tour de France champion Cadel Evans, was considered among the big favourites for the wind-hit race against the clock, which handed him his first Grand Tour stage win.
As well as winning the under-23 world title for the time-trial in 2010, Phinney has twice won gold in the world championships individual pursuit - an event which is no longer on the Olympic programme - in 2010 and 2011.
He is also the son of former cycling champions. Mother Connie Carpenter was the Olympic road race champion in 1984, while father Davis Phinney was the first American to win a stage at the Tour de France, in 1986.
Phinney is not considered a contender for the overall title, but on the first day the real contenders began counting the cost of their losses and gains.
Defending Giro champion Michele Scarponi of Italy finished 1min 06sec off the winning pace, thus giving up 27sec to former champion and compatriot Ivan Basso and 30sec to Czech contender Roman Kreuziger.
Spanish climbing specialist Joaquim Rodriguez, meanwhile, was only four seconds off the pace of Basso, while Luxembourg's Frank Schleck, a late addition by his RadioShack team, was 20sec adrift of Basso.
The race resumes on Sunday with the wind expected to play a role when the peloton tackle 206km around Herning, much of which will be along the coast.
STAGE RESULTS 1. Taylor Phinney, United States, BMC Racing, 10 minutes, 26 seconds.
2. Geraint Thomas, Britain, Sky Procycling, 9 seconds behind.
3. Alex Rasmussen, Denmark, Garmin-Barracuda, :13.
4. Manuele Boaro, Italy, Saxo-Bank, :15.
5. Gustav Erik Larsson, Sweden, Vacansoleil, :22.
6. Ramunas Navardauskas, Lithuania, Garmin-Barracuda, :22.
7. Brett Lancaster, Australia, GreenEdge, :23.
8. Marco Pinotti, Italy, BMC Racing, :24.
9. Jesse Sergent, New Zealand, RadioShack-Nissan, :26.
10. Nelson Oliveira, Portugal, RadioShack-Nissan, :27.
