Calgary's Ellen Pennock crashed during the bike portion of the event and suffered a suspected broken collarbone while Sarah-Anne Brault of Winnipeg dropped out during the run.
England's Jodie Stimpson won the race to earn the first gold medal of the Games. She completed the 1,500-metre swim, 40-kilometre cycle and 10-kilometre run in a time of 1 hour, 58 minutes, 56 seconds.
Sweetland finished five seconds behind, and England's Vicky Holland came in 15 seconds back to take the bronze.
Stimpson and Sweetland were tied for the lead after the bike leg, with Holland in fourth.
Sweetland, 25, has struggled with injuries in recent years, but she peaked at the right time. Less than two weeks ago, she reached the podium in a World Triathlon Series event for the first time in her career, finishing third in Hamburg.
3 Canadians in men's race
The men's triathlon was scheduled for later in the day; one of 20 gold medals to be presented on the first day of competition.
Triathlon Canada plans to have its three men's entries work as a team. Matthew Sharpe, a 22-year-old from Victoria who's considered a strong swimmer and cyclist, will try to influence the pack to make things easier on Ontarians Kyle Jones and Andrew Yorke.
Jones, 29, placed 25th at the London Olympics and was the top Canadian in the Grand Final of the 2013 World Triathlon Series, placing 19th. He finished 15th at the London stop of the World Triathlon Series this year.
Yorke, 25, was an Olympic alternate whose career-best finish in a World Triathlon Series event is 15th.
Cochrane into swim final
In the pool, defending men's 400-metre freestyle champion Ryan Cochrane of Victoria finished second in his heat, advancing to the final later in the day.