Muenzer, 38, beat Tamilla Abassova, 17 years her junior, in the best-of-three final of the women's sprint.
No Canadian had previously won a medal of any colour in the short history of women's Olympic cycling and while the Canadian men have won five on the track, none were gold.
The Canadians had also never won a gold medal in either Olympic road racing or mountain biking and Muenzer joins a small band of compatriots, most notably Curtis Harnett between 1984 and 1996, to have stepped on to an Olympic cycling podium.
"I'm on cloud nine. It's unreal," she said.
"To be up there with the other great Canadian cyclists is an honour. It hasn't sunk in yet. If you'd have told me 10 years ago it would take this long I'd have challenged you on that."
"We've been working for this week for five years and this week has been my fastest week, my strongest week and my smartest week of racing ever."
Abassova took the silver and Anna Meares of Australia beat Russian world champion Svetlana Grankovskaya to add a bronze medal to the gold she won in the 500-metre time trial.
The men's final was an enthralling contest between Bayley, famed as a junk food fanatic with a weakness for deep fried chicken, and Bos, who celebrated his 21st birthday on Sunday.
Bayley was behind as the riders shot round the final bend of the wooden track but produced an explosive final burst of speed to win by little more than the width of a tyre.
"Just to cross the line on that last one, my head just stopped," Bayley said. "I didn't know what was going on. All I know is that I crossed the line and looked at him and thought, 'Yeah, I'm in front. Wicked'."
Germany's Rene Wolff beat France's Laurent Gane for the bronze, compounding a miserable Olympics for the traditionally powerful French cycling team.
In the day's other final, unheralded 19-year-old Mikhail Ignatyev won gold for Russia in the men's points race.
Defending Olympic champion Joan Llaneras of Spain took silver while veteran Guido Fulst, part of Germany's victorious sprint team from the Barcelona and Sydney Games, won bronze.
Ignatyev finished with 93 points to Llaneras' 82 and Fulst's 79. Riders get points for lapping the main pack or for placing in the sprints, which are held every 10 laps. (Additional reporting by Alan Crosby and Alan Baldwin)