Danielson, who started the stage in 11th place, jumped to sixth overall after completing the 210.1-kilometre ride from Gunnison to Aspen in five hours, two minutes and six seconds for his first win since 2009.
"With two kilometres to go, I didn't think I was going to win," said Danielson, who finished eighth in the 2011 Tour de France but suffered two fractured shoulders after crashing out of this year's event. "I wanted to look back, but I didn't and it worked."
Danielson had about a two-minute advantage while cresting the final climb but the field narrowed the gap in over the mostly downhill waning miles.
Damiano Caruso of Italy finished second and Jakob Fuglsang of Denmark was third, both only two seconds behind Danielson along with the rest of the main field.
Vande Velde, who started the stage second overall but in the same time as overnight leader Tejay van Garderen, finished ninth in the stage while Van Garderen placed 12th after a ride that included two climbs approaching 4,000 metres.
The two riders have the same overall time and same point totals but Vande Velde assumed the race lead based on his higher finish in the third stage.
Van Garderen finished a few bike lengths ahead of Vande Velde during Tuesday's second stage but race officials gave both riders the same time. Van Garderen's team protested the result with a decision expected Thursday.
Thursday's fourth stage of the seven-day event is a 156.5-kilometre ride from Aspen to Beaver Creek.