Sinclair, from Burnaby, B.C., scored in the 73rd minute to salvage the tie.
Linda Sembrandt scored in the 57th minute for Sweden, which lost 1-0 to Canada on Tuesday.
"It was an important goal for our team," said Sinclair. "We wanted to get two results in a row against Sweden and we had quite a few chances tonight and it was nice to put one away when we needed it."
Head coach John Herdman said he was impressed with his team's resolve, especially in the second half.
"As a group, we know how to stick together when the time's right and watching them in that last 30 minutes when both teams were tired on a sunny day and it's 1-1, both teams might have said 'look, let's play for a draw' but we didn't.
"We pushed our fullbacks on and I'll always play like that. These girls don't want it any other way. We just want to win football matches."
The game was the last match of the year for the national team as they continue to prepare to host next year's FIFA Women's World Cup.
The official draw for the 2015 tournament will take place Dec. 6 in Ottawa.
"We want to know who we're facing in the World Cup and who we need to start preparing for," said Sinclair. "I'm excited to be a part of it and hopefully I can bring some luck to our team."