Canada held off early pressure from China and was rewarded when Leon, who was making her debut with the team, scored in the 75th minute.
The forward from Maple, Ont., intercepted a stray pass and charged to the edge of the penalty area before firing a hard shot past the Chinese goalkeeper.
Canadian head coach John Herdman said he was surprised by his team, who he expected to struggle after a layoff following the London Games.
"I didn't think we would come this far today," said Herdman. "China could have scored a couple goals in the first half if we're honest, but in the second half we took the performance.
"There was some really good football played in the style we've been working on. It was a good step forward."
Canada is playing without star striker Christine Sinclair, who is serving the first three games of a four-game suspension.
The Burnaby, B.C., native was penalized following Canada's heartbreaking 4-3 semifinal loss to the United States at the Olympics when FIFA ruled she showed "unsporting behaviour towards match officials after the match."
In other action Saturday, Norway defeated South Korea 2-0 in the other game.
Canada next plays South Korea on Monday.