The teams meet again Saturday in Victoria, British Columbia.
Morneau tallied in the 62nd and 84th minutes to carry the Canadians, preparing for the CONCACAF Women's Gold Cup, before 2,653 at Swangard Stadium. Former Atlanta Beat midfielder Amy Walsh set up the first goal.
Boston Breakers goalkeeper Karina LeBlanc stopped Australia's Kelly Golebiowski on a breakaway shortly after Morneau's first goal. Atlanta striker Charmaine Hooper created two strong scoring chances during the first half, which was dominated by Canada.
Midfielders Olivia Hohnke and Tal Karp made their debuts for the Matildas, who will face the United States, Italy and Russia in the U.S. Women's Cup that begins Sunday.