The Garmin-Sharp rider raced to the finish line in Telluride ahead of Alessandro Bazzana (UnitedHealthcare Pro Cycling Team) in second and Damiano Caruso (Liquigas-Cannondale) in third.
Farrar, who had not won since July 2011 when he secured his first individual Tour de France stage victory, takes the early overall lead of the race in Colorado.
The American benefited from some good work over the mountains from his team-mates before sprinting to victory at the end of the 202.1km stage that started in Durango.
"I really had to turn myself inside out to make it over (Lizard Head Pass)," Farrar said. "I knew today could possibly be a sprint but I really wasn't sure I had the legs to make it, so I'm pretty happy to pull it off.
"Our home as a team is in Colorado, so we take this race really seriously, and to win here is huge. For me personally I have had kind of a disaster of a season so this means a whole lot to me to finally get a win."
The race continues on Tuesday with a 159.6km trek from Montrose to Crested Butte. The undulating stage features three category 3 climbs, including the final two-mile ascent to the finish.