The USA look set to win the SheBelieves Cup after seeing off Brazil, while Canada left it very late against Argentina.
Lindsey Horan set up both goals for the US, although the second came with just two minutes remaining,
Christen Press received a pass in the 11th minute and advanced into the corner of the box before shooting high into the net.
Ludmila looked to have an opportunity to level in the first half but Crystal Dunn made a great sliding tackle inside the penalty area, then from a late free kick, Horan knocked the ball up for Megan Rapinoe to volley home.
The result saw keeper Alyssa Naeher make a new USWNT record of ten consecutive clean sheets.
A win or draw against Argentina on Wednesday will see the USA clinch tournament title.
Canada edge Argentina with 92nd-minute winner
Sarah Stratigakis scored in added time as Canada posted a narrow 1-0 victory over Argentina, for their first points of the tournament and Head Coach Bev Priestman’s first win.
Argentina had come closest to scoring, when midway through the second half, Soledad James headed against the crossbar.
The winner came via a Janine Beckie free kick, which was played on by Jessie Fleming into the path of Stratigakis who slid the ball into the net.
Canada finish up against Brazil on Wednesday to decide second place.