Yankey scored the winning goal with a neat half-volley in the 70th minute but the Three Lions could have won by a greater margin, having created the better chances throughout.
England, winners of this competition in 2009, reached the final by beating Italy and New Zealand in the group stage, either side of a 4-4 draw with Scotland.
The Canadians pressed high but it was the Three Lions who fashioned the better chances early on.
Anita Asante and Eniola Aluko should have put England ahead in the first half while Rachel Williams and Ellen White both had chances after the break.
Hope Powell's side were on top for large spells against the three-time Cyprus Cup winners and this victory will give the national coach a modicum of revenge after her Team GB side were knocked out of London 2012 by John Herdman's charges.
The win will no doubt give England confidence ahead of Euro 2013 in Sweden this summer, while the two sides will meet again in a friendly at Rotherham on Sunday 7 April.