It was Canada who started the match the better, with Christine Sinclair causing a host of problems with her direct running.
The opening half turned in an instant, however, when Marie Hammarstrom stuck from close range to send Sweden into the lead.
It was quickly two just moments later when Sofia Jakobsson finished off a sweeping move, with Canada failing to come to terms with the turnaround.
The chances continued to come late in the half for Sweden, with Kosovare Asllani firing wide, but it was Canada who got back into the match when Melissa Tancredi struck from close range.
Tancredi so nearly levelled after 48 minutes, but Hedvig Lindahl made a smart save with her legs, before Filigno's shot was blocked.
Chances continued to fall for Canada in the shape of Sinclair, while Lotta Schelin had an effort which whistled past the post for Sweden.
The equaliser eventually came 10 minutes from time when Tancredi headed past Lindahl, as they completed the turnaround to book their spot in the latter stages.