Tuft, riding for the Orica-GreenEdge team, finished the 17.4-kilometre time trial in 20 minutes 25 seconds. American Taylor Phinney was second, five seconds behind the Canadian. Lars Boom of the Netherlands was third, six seconds behind Tuft.
"When I came across the line and saw my time, I was pretty surprised," Tuft said. "I was hoping to have a really good time trial, but I didn't expect to be in the leader's jersey at this point in the race.
"It's a great feeling."
With the win, the 35-year-old Tuft will carry a four-second overall lead into the final stage Sunday, a 214.5-kilometre trek.
Phinney had posted the fastest time of 20:30 in the time trial but at the intermediate checkpoint, Tuft found himself less than a second behind the American. He continued his torrid pace to post the five-second advantage upon crossing the finish line.
"This morning when I did a little warmup, I knew it was going to be a good ride," Tuft said. "With how good I felt, I knew if I put everything down that I had, I could be in contention for a top-three on the stage."
Tuft said he took a rather different approach to Saturday's ride.
"A lot of riders put an emphasis on the first half of the course," he said. "We went out in a headwind section and returned with a tailwind.
"They might not have realized it was difficult coming back as well. I still had a good amount of gas in the tank for the second half of the effort, and I think that's where I made up quite a bit of time."
Spain's Alberto Contador, a former Tour de France winner returning from a doping ban, finished seventh Saturday to stand 10th overall, 49 seconds behind Tuft.