Tom Maher’s side led for most of the final quarter after pegging Canada back, who were in front for most of the match, but were unable to drive home their advantage and eventually lost 73-65.
Great Britain always tried to stay within three points of Canada, as they looked to bounce back from defeat to world number two Australia in their opening fixture.
Australian-based Jo Leedham was at the centre of everything, but her shooting needed to improve if Team GB were to close the gap.
With Great Britain scoring everything from the free throw line, they were unfortunate to trail into the interval 36-32, with Natalie Stafford their top scorer.
The hosts started the second half well and managed to claw back to within one point, but some quick breaks and good movement meant Canada were scoring consistently under the basket.
Great Britain struggled to cope with the size of Krista Phillips, but a much better performance, an increased shooting percentage and some great play from Leedham, saw them head into the fourth quarter just two points down.
With their noses in front, Great Britain worked hard to put Canada under pressure, and Julie Page stretched Team GB’s lead to four points midway through the final quarter.
In a tense finish, the sides were level as they headed into a timeout before a superb shot from outside the arc for Canada sent them ahead.
They then turned on the accelerator and three quick baskets, including one three pointer, left the hosts seven points behind.
Canada used their experience to see out the game, as Leedham desperately attempted to finish from the three-point line, before time ran out with Canada winning by eight points.
The manner of the defeat will be a cruel blow to Great Britain and they will need to pick themselves up before they face two-time Olympic bronze medallist Russia.
The French women's basketball team produced a stunning overtime upset of three-times silver medallists Australia on Monday in a wildly entertaining game in the Olympic tournament.
The 74-70 victory for France marked the first Olympic defeat for Australia against a team other the United States since 1996 and gave the winners a 2-0 record in preliminary play while dropping the losers to 1-1.
"It was a big, big victory because it was against a big team like Australia," French captain Celine Dumerc said. "It was not a target for us at the beginning of the tournament but we played with desire and energy to get the win."
The tightly played contest had a thrilling moment that went in Australia's favour at the end of regulation time.
After France had taken a 65-62 lead with three seconds left in the game, Australian Belinda Snell heaved up a miracle shot from beyond the midcourt line that went through the hoop with no time left on the clock to send the game into overtime.
"I screamed for it (the ball) and I threw it up there," Snell said about her sensational game-tying shot.
France led by as many as 13 points in the game and Australia led by as much as eight but the final minutes produced nail-biting drama.
"Whoa. That's basketball as we like to play it," France's Isabelle Yacoubou said. "There were some mistakes. There were some amazing shots."
Emilie Gomis, who ignited the French attack with 14 points over the first five minutes of the second half, led France with 22 points and Dumerc contributed 13.
Suzy Batkovic led the way with 17 points for Australia, who were hurt by having both Lauren Jackson and Elizabeth Cambage foul out.
Australian captain Jackson scored 13 points in just under 26 minutes on the court, while Cambage had 12 in less than 22 minutes.
"As a spectacle for the fans it was a great game, but for us it was a bit of a shame," said Jackson.
Dumerc said it was too soon for France to dream they could top Group B for a favourable position in the quarter-finals.
"We started greatly with two wins against teams that are on our level or even better than us," the captain said after the rousing win that followed an opening 73-58 victory over Brazil.
"But we still have three games to play before we can even think if we can top the group."
The US women's basketball team, evoking memories of the men's Dream Team of 1992, put on a hoops masterclass in routing African champions Angola 90-38 at the Olympics.
It took a little while for the Americans to get in synch, but once they did the reigning four-times Olympic champions put on a fastbreak show to extend their Games winning streak to 35 in a row.
The last time the US women lost at an Olympics was 20 years ago in Barcelona when they came away with the bronze at the Games where the newly-invited NBA stars swept to the gold beginning with a 116-48 romp over Angola's men's team.
"It's important that in a game where you know that there is that disparity, that you just do the things you need to do to be a better team," US coach Geno Auriemma said.
Candace Parker led a balanced US attack with 14 points on Monday while Sonia Guadalupe was top scorer for Angola with 11 points as they lost again in their second outing.
Angola coach Anibal Moreira, who played with the men's squad that faced the US Dream Team in Barcelona, said he wanted his players to have fun.
"We decided we wanted just to enjoy the game, because of the difference between the standard of the US team and ourselves," he said.
"We feel a lot of pride in being able to have the opportunity to play against such a team, who are the idols of many of our players. We hoped to get to 50 points but we didn't quite make it."
China improved to a 2-0 record with an easy 83-58 win against Croatia; Russia (2-0) won 69-59 against Brazil (0-2), and Turkey (2-0) won 61-57 over the Czech Republic (0-2).