The midfielder from Oakville, Ont., scored in the 92nd minute as Canada beat France 1-0 in the women's soccer bronze-medal game at the London Olympics on Thursday.
The bronze combined with a silver medal from veteran wrestler Tonya Verbeek increased Canada's medal haul to 16.
After being forced to play defence for most of the second half Thursday, Canada capitalized on a rare opportunity when Matheson's shot off a deflection beat goalkeeper Sarah Bouhaddi and stunned the French.
"It feels amazing. It feels unreal," Matheson said. "It feels like a dream."
The bronze is Canada's first Summer Games medal in a traditional team sport since winning silver in men's basketball in 1936.
Later Thursday, wrestler Tonya Verbeek won silver in the 55-kilogram category after losing to Japan's Saori Yoshida in the gold-medal bout.
"I promised going into the Olympics I would give everything and the result would take care of itself," Verbeek said. "Wrestling is an awesome sport, it's done wonderful things in my life and I have three Olympic medals.
"The Games is not just about being here in the stadium, it's about the qualification and the pushing through."
Verbeek, of Thorold, Ont., won bronze in Beijing four years ago and silver at the 2004 Games in Athens.
"I felt a lot of belief in myself and I felt good going into the finals. I said to myself, 'This is my time', but sometimes it doesn't work out that way," said Verbeek, who was competing at her last Olympics. "I feel really great, I have my family and friends here.
"I promised myself before this competition that I was going to enjoy myself and I feel I did that today."
Canada has won five medals in the last two days as the country continues to creep closer to the 18 it won four years ago in Beijing. With one gold, five silver and 10 bronze, Canada is tied for 11th with the Netherlands in the overall medal count.
The bronze-medal result in soccer should help Canada recover from an emotional 4-3 loss to the United States in a semifinal marred by controversial officiating.
France, which ousted Canada from last year's Women's World Cup in a dominating 4-0 performance, controlled play with several quality chances in the second half, including shots that hit the crossbar and the post.
But Matheson, a five-foot midfielder from Oakville, Ont., scored to lift Canada onto the podium and give the team something to build on ahead of 2015 when it hosts the Women's World Cup.
"I think I'm in shock. There's been a group of us that has been on this team for a long time that have experienced the highs and lows of international soccer and nothing compares to this," Canadian captain Christine Sinclair said. "I don't think any of us at the end of last year's World Cup would have thought this was possible."
In other Canadian results:
— Damian Warner of London, Ont., built on a strong first day in the decathlon to finish fifth overall.
— Roseline Filion of Laval, Que., finished 10th in the final of the women's 10-metre platform dive, while Montreal's Meaghan Benfeito was 11th.
— Calgary wrestler Leah Callahan lost her opening match in the 72-kilogram category to Burmaa Ochirbat of Mongolia and was later eliminated.
— Emilie Fournel of Lachine, Que., was sixth in the B final of the women's K-1 500 kayak race. The result placed Fournel 14th overall.
— Toronto's Zsofia Balazs finished 18th in the women's open-water swimming event at Hyde Park.
— Canada's women's synchronized swimming team are fourth after the technical routine ahead of Friday's final events. They scored 94.4 points, trailing first-place Russia (98.1 points).
— Tory Nyhaug of Coquitlam, B.C., failed to advance to the semifinal of the men's BMX event.
— Jessica Smith of North Vancouver, B.C., failed to move on to the final in the women's 800 metres.
— Vancouver's Elizabeth Gleadle finished 12th in the women's javelin.