Armstrong, the last of 103 riders to start, fell hard at the turnaround, putting her London Olympic hopes in doubt.
Whitten, an experienced Canadian track rider, finished in four minutes nine seconds.
She finished just ahead of Victoria's Gillian Carleton. Winnipeg's Clara Hughes was third.
Armstrong, from Boise, finished about 10 seconds behind Whitten. The American was crying and holding her left shoulder after she climbed off her bicycle. Her husband, Joe Savola, said she would have surgery Thursday night, and hasn't ruled out competing in the London Olympics, if she's chosen for the team.
USA Cycling will make its selections June 15.
"She's the fastest time-trial rider in the world," Savola said. "She would have broken four minutes. She was flying, she was taking a chance."
After the race, Whitten told The Associated Press that sharp turns on the course forced her to slow at several sections, including the turnaround.
"There were some technical sections where I thought I lost a little time," she said.
Whitten races for Team TIBCO, a California-based team that had $120,000 worth of bikes and equipment stolen from the team trailer a day before the race. All of the bikes were recovered.
"It was definitely not a good feeling (Wednesday) morning when we came down to breakfast," said Whitten, whose road bike was among those taken. She was all smiles after winning the stage just a day later.
Following the race, Whitten, Carleton and Hughes were shocked and saddened to learn at a news conference the extent of Armstrong's injuries.
Hughes said she fell on the same turn as Armstrong during the warm-up for the race. She said she slowed for the turnaround during the race, but only a little.
"My easy is probably on par with other people's hard, so I don't think I lost any time," Hughes said.
The Exergy Tour continues Friday, with a 123.4-kilometre ride through Idaho wine country near the Snake River.
The five-day event concludes Monday.