– For John Shuster, Monday’s big victory over Canada was delivered by the thinnest of margins. Nina Roth had a little more breathing room, as her team needed only eight ends to beat China.

Both U.S. curling teams kept their Olympic playoff hopes alive with superb performances Monday at Gangneung Curling Centre. Shuster’s thrilling final shot gave the American men a historic 9-7 victory, marking the first time the U.S. has beaten Canada at the Olympic Games.

Roth’s team edged Denmark 7-6 in the morning session, then routed China 10-4 in the evening to win consecutive games for the first time in the tournament.

The nine-game round robin ends Wednesday, with the top four teams moving on to the playoffs. The U.S. men (3-4) were in a three-way tie for fifth place after Tuesday’s morning session. The U.S. women (4-3) were tied for fourth with Great Britain.

Shuster shook off his shooting woes Monday in an extra-end victory. The Minnesota skip needed his final shot to knock out a Canadian stone and come to rest nearest the button; first, it had to get past a guard, a rock that Canada had placed to block the path. Shuster’s shot barely sneaked past the guard, then bumped out Canada’s scoring stone and stopped on cue to end his team’s best game of the tournament.

“I knew [the last shot] was a tiny bit tighter line than I initially wanted it to be out of my hand,’’ Shuster said. “I gave a scream for Matt [Hamilton] to sweep, and it got by by half an inch.

“It was good to bounce back. Let’s just hope it’s not too late.’’

‘‘We kept ourselves in the mix and got a big win over an extremely good curling team. I’m extremely proud of the way the team came together and played.’’

Like the U.S. men did in the Canada game, the U.S. women came through on the last rock to get past Denmark as Roth drew to the 4-foot for the winning point. They quickly overpowered China with three points in the first end and added four points in the third, zooming to a 7-1 lead. China could not make up much ground and conceded after eight ends.

“It’s our first two-win day, and it feels amazing,’’ said Tabitha Peterson of Eagan, the U.S. vice-skip. “I think we’re rolling. We’re making a lot of shots and calling the ice right. It feels really good out there.’’

Both teams end the preliminary round with difficult matchups. To have a chance at the playoffs, the men must win their final two games, against Switzerland on Tuesday night and Great Britain on Wednesday afternoon. The Swiss are ranked third in the world and are in second place in the standings, while the Brits are third in the round robin.

The women play Tuesday against Korea, which leads the round robin, and finish Wednesday against Sweden, which is tied for second.

Shuster’s team was especially grateful to recover from back-to-back losses Sunday, which severely damaged its playoff hopes. Vice-skip Tyler George of Duluth said the foursome finally showed its best form in the victory over Canada.

“We just felt like we had nothing to lose,’’ George said. “Let’s go out and relax, let it fly and whatever happens, happens.’’