Swedish skip Anette Norberg suffered a few early miscues but her side fought back to win 7-6 in the extra end after Bernard blew chances in the final two ends to seal a home victory in front of a boisterous crowd.
"We got nervous after the fifth end and we got shaky, and she (Bernard) got shaky in the last two ends," Sweden's Cathrine Lindahl said. "We thought it was over. I'm so happy."
Sweden retained their title and became the first team to win two golds in Olympic women's curling.
With Canada leading going into the 10th end, Bernard failed to nail her last rock, allowing Sweden to score two and tie it up at 6-6. It was Bernard's final throw in the subsequent end that ended her dream of gold on her Olympic debut.
The 43-year-old had to throw her rock hard and accurate enough to blast two Swedish stones out of the house.
It cleared one but did not have sufficient angle or strength to clear the second, leaving the Swedes to celebrate a win which minutes earlier had seemed unlikely.
"I rubbed it and I missed," a crushed Bernard said. "It was so close. "It was one of those shots I will not forget."
Norberg said she knew something was amiss as soon as the rock left Bernard's hand and her team mates jumped to action.
"I heard them sweeping all the way down so I understood that it was curling a lot, and the spot where it curled wasn't where it was aimed," she said. "Suddenly I understood that maybe she wasn't going to do it."
Sweden's victory, with the country's King Carl Gustaf looking on, robbed Canada of one gold on which they were banking.
The Olympic hosts won all but one of their qualification games on the strength of Bernard's accuracy.
She also had the backing of an uncharacteristically noisy curling crowd, some of whom yelled "We love you, Cheryl!" before she made her throws.
The Swedes gathered steam throughout the tournament, winning their last three games. Norberg, 43, showed little emotion on or off the ice. She said she was unaffected by the crowd because she was in her "own bubble" when playing well.
She needed that early in the match to block out heckling by fans when she prepared her throws.