Canada needed a stoppage-time spot-kick to defeat China, while a stunning goal from Lieke Martens saw Netherlands win on the opening day.
Hosts Canada started the 2015 Women's World Cup with a victory but only after captain Christine Sinclair converted a penalty in the 92nd minute.
Canada dominated the opening match of the tournament against China in Edmonton but needed Sinclair's late spot-kick to secure a 1-0 win in front of a record crowd of 53,058.
The decisive moment came when Zhao Rong blocked Canada substitute Adriana Leon in the penalty area with an arm to the face, with Sinclair striking her attempt in off the post, which saw the home crowd erupt.
Canada finished the match with 14 shots to just five from China, while the hosts had 62 per cent possession as well.
The crowd at Edmonton Commonwealth Stadium was the largest ever to watch a Canadian national team.
"It was an amazing atmosphere to go out and play this opening match of the World Cup in front of 50,00 plus fans," Canadian midfielder Sophie Schmidt said.
"The Chinese sat back and challenged us to come at them, and finally something went our way. Then Sincy [Sinclair] - Oh Captain, my Captain - came through and I'm just glad she put that in."
The opening match was followed by a 1-0 win for Netherlands over New Zealand, with Lieke Martens producing an early contender for goal of the tournament as the Dutch won their maiden World Cup game.
Martens cut in from the left wing in the 33rd minute before launching a right-footed shot into the top corner, sending the Dutch alongside the Canadians at the top of Group A.