The 23-year-old Sagan, riding for the Italian-based Cannondale, completed the 106.1-mile stage from Breckenridge to Steamboat Springs in 4 hours, 4 minutes, 18 seconds for his 17th win of the season.
Sagan, a four-time Tour de France stage winner, remained third overall - 11 seconds back after claiming the 57th win of his career.
''The team was very good and I felt good today,'' said Sagan, who was 17 wins this season. ''I felt sorry for Jens (Voigt), but when the team went to the front, there was only one way he could win and we caught him with three kilometers to go.''
Morton, riding for Garmin-Sharp, finished 30th in main field in the same time as the winner to retain a 2-second lead over Mathias Frank, the BMC rider from Switzerland.
''I was a new experience for me,'' said the 21-year-old Morton, a first-year pro who earlier this month won his first pro race in the Tour of Utah. ''It was a lot of fun.''
The third stage included at least three crashes, including three riders falling in the final two miles. Injuries have not been reported by race officials.
The 41-year-old Voigt, the oldest rider in the field, escaped from a lead group of five with about 40 miles left in the stage and built nearly a 2 1/2-minute lead.
But Voigt, a two-time Tour de France stage winner, was caught by the field within the final two miles.
Slovakia's Luka Mezgec of Argos-Shimano was second in the stage, followed by Canada's Ryan Anderson of Optum-Kelly Benefit.
Defending titlist Christian Vande Velde finished 18th and was 17th overall, trailing by 46 seconds.
The weeklong race continues Thursday with the 102.9-mile leg from Steamboat Springs to Beaver Creek. The stage features five climbs, including one slightly longer than a mile to the finish to Beaver Creek Village.
The event's third edition continues through Sunday with 72.4-mile Denver Circuit Race.