Sutherland, who rides for the United States-based UnitedHealthcare team, won the stage from Golden to Boulder - the final mountain stage - in four hours six minutes 12 seconds.
Leipheimer began in the stage in fourth place and trailing by eight seconds but bolted to the front of a small chasing group within the final three kilometres.
"I can't take credit for planning it like that, but obviously it was in the back of my mind to do that," said Leipheimer, who has finished in the top 10 of the Tour de France four times.
"The guys have gone above and beyond what they could do this week."
The week long, second-year race concludes on Sunday with a 15.3km individual time trial in Denver, Colorado.
"I'm not comfortable, I've got some great guys breathing down my neck," said Leipheimer, who holds a nine-second margin over countryman Christian Vande Velde, a former race leader who began the day in second via a tie-breaker.
American Tejay van Garderen, the previous race leader, faltered in the final mile, finished 11th in the stage and is now third overall, trailing by 21 seconds.
Sutherland, who has lived in Boulder for several years, emerged from a lead group at the base of the final climb, about five kilometres from the finish, and rode alone the rest of the way.
"I know this climb well enough that I knew I had to go at the bottom," Sutherland said. "I know where to go easy, I know where to go hard. I've done this climb, I don't know how many times. But this was the most beautiful one I've done."
Fabio Aru of Italy was second in stage six, trailing by 20 seconds. Jens Voigt of Germany was third, another six seconds back.