ZURICH — Sandis Vilmanis scored two empty-net goals and Latvia upset the United States 4-2 to hand the defending champion its third defeat at the ice hockey world championship on Saturday.

Deniss Smirnovs’ goal early in the third period gave Latvia a 2-1 lead and set up a wild ending.

The Americans pulled goaltender Devin Cooley for an extra attacker but Vilmanis scored with 1:02 left to make it 3-1.

The U.S. struck back — again with six skaters — when Matthew Tkachuk set up Mathieu Olivier to cut the deficit to one from the slot with 0:51 remaining.

Vilmanis sealed the victory, though, when he netted his second with 42 seconds to go.

Latvia had opened the scoring in the first period when Haralds Egle connected at 8:47 with his team’s second shot on goal.

Tkachuk’s power-play goal — his first at the worlds — tied it at 1-1 with 5:12 remaining in the middle period. The two-time Stanley Cup winner and Olympic champion played only his second career game at the worlds after joining teammates on Tuesday.

The loss left the U.S. fifth in Group A, one point behind Latvia. The Americans have two group stage games left — against Hungary on Monday, and Austria on Tuesday.

In Group B in Fribourg, Denmark blanked Slovenia 4-0 for its first win.

Later Saturday, host Switzerland meets Hungary, and Austria plays Germany in Group A in Zurich. In Fribourg, Czechia plays Slovakia, and Sweden faces Norway.