It's the first gold for Canada's women curlers in the country's second most popular sport since 1998, when curling returned to the Olympic program. Sweden's women had won gold at the last two Olympics.
Britain beat Switzerland 6-5 earlier Thursday to win the bronze medal.
The winning moment came when Jones released her first rock in the last end. Before it bumped a Swedish stone out of the house, and clinched the win, the skip was on her knees with her hands on her face at the other end of the ice.
She then bounded down the ice and, with a joyous whoop, huddled with her teammates and jumped up and down.
The championship means Canada's women curlers have finally come out of the shadow of their men's teams, who have won gold at the last two Olympics. But this victory wasn't pretty.
Canada won the teams' round-robin game 9-3 in eight ends but the championship game was much closer, with tension high and the pressure clearly getting to a previously unruffled Canadian team.
Save for a rare clanging cow bell, the atmosphere in a three-quarter-full Ice Cube Curling Center where there was a large Canadian presence was subdued with three scoreless ends out of the first seven hardly making for gripping viewing.
Having won world and multiple Canadian titles, Jones was looking to fill her resume with Olympic gold. She had been the top female curler in the tournament, and she needed to be at her best in the final as teammates Jill Officer and Kaitlyn Lawes produced poor displays early on.
Sweden squandered a great chance for four points and a 5-3 lead in the fifth end when Maria Prytz failed to make a clean double takeout and was fortunate in the end to claim two points to tie the score at 3-3.
"Terrible end," Jones uttered to Lawes.
After blanks in the sixth and seventh ends, the tension apparently got to Jones when she came up short with a draw to the button in her last shot. Canada got the point after a measurement but Sweden had an opportunity to counter.
In the crucial ninth end, Canada had four rocks in the house surrounding a sole Swedish stone. Maria Prytz, shooting last for the Swedes, could have picked up two points but her shot bumped into one of her own rocks and handed Canada two steals.
The last end was a formality and Canada's women ended a 16-year wait for gold.