Wales needed to win a doubles decider as they ended Scotland's brave title defence with a 2-1 victory at the World Cup of Darts.
Gerwyn Price produced a superb 104.6 average as he defied a 121 finish from John Henderson to claim a 4-2 win in the opening Singles match.
Robert Thornton showed his class to win the second Singles tie by the same scoreline against Jonny Clayton to create the day's first doubles decider, but it was Wales who progressed with a superb 4-0 win.
"We showed good teamwork there," said Price. "I think we were more consistent in the Pairs today and you can't argue with a 4-0 win.
"I think it could be a good year for us. We need to concentrate on our own games and hopefully we can bring our A-game tomorrow, but I don't think anyone has won a tournament without having a little bit of luck."
Clayton added: "Gerwyn's a brilliant captain and he told me to get my head back up because we had another game to go and we came through it.
"I let Gezzy down today with my game against Robert. I was confident going into it but Rob did the job and I had to lift my head for the Pairs.
"I'm feeling good and Gez is playing awesome. It's a big game tomorrow, and I think if we both bring our A-games, we're going to win that."
Australia saw off Poland 2-0 to book their place in the quarter-finals, although Simon Whitlock was left sweating as he edged out Krzysztof Ratajski in a thrilling singles tie.
A high-quality singles tie saw Whitlock finish 117 as the game went all the way to a deciding leg, in which Ratajski hit two 180s but missed a dart at the bull for victory, allowing the Australian in to finish a last-dart double ten.
Heta then opened his singles game with Krzysztof Kciuk with two 180s in a ten-darter, before going on to average 99.99 in a 4-1 victory to ensure Australia's place in Sunday's final stages.
"That was a great, solid performance from the pair of us," said Whitlock. "We both performed amazingly well but I was really pushed all the way by Krzysztof.
"It's such a short format that anyone can win this on the day, and we believe in ourselves. We're very evenly matched as a pair and as much as I want to win every tournament, it means a little bit more when you're playing for your country."
Four-time champions Netherlands will take on Germany in another eagerly-awaited tie after they defeated Spain 2-0 - although Jesus Noguera paid for missing six match darts to force a Doubles decider.
World number one Michael van Gerwen averaged almost 102 and hit four doubles from seven attempts in a whitewash of Toni Alcinas, before Noguera came from a leg down against Danny Noppert to lead 2-1 and 3-2.
Noppert forced a decider, with Noguera being first to a finish only to see six match darts go begging as the Dutchman stepped in to post double ten to secure a spot in the last eight.
German pair Gabriel Clemens and Max Hopp continued their impressive start to the tournament by moving into the quarter-finals for the loss of only one leg as they defeated Greece 2-0.
Clemens defeated John Michael 4-1 as he took out a 130 finish in a strong display, before Hopp whitewashed Veniamin Symeonidis 4-0 as they backed up Friday's 5-0 first round defeat of Finland in style.
"We're very happy to be in the quarter-finals and it's about time I made it into the semi-finals!," said Hopp, who has lost at the last eight stage three times previously.
"We are quite fluent and enjoying our games, and I can't wait for tomorrow. We have a great team spirit and are a good team together."
Canada won through to their first World Cup of Darts quarter-final since 2016 with a 2-0 defeat of New Zealand, who had been bidding to reach the last eight for the second straight year.
Jeff Smith gave Canada the early advantage as he defeated Haupai Puha 4-1 in the opening singles tie, sealing victory with a 100 finish.
Cody Harris put New Zealand 2-0 up in the second singles contest, but Matt Campbell produced a stirring fightback to win four straight legs, all between 13 and 15 darts, to take a 4-2 win and put Canada into Sunday's final day.
"We're thrilled to win," said Smith. "To be through without having to play the doubles match is awesome and it shows what a partner I have in Matt
"We've never been in the semi-finals before but I've got a talented player alongside me. Matt can beat anybody and we'll back ourselves in the doubles if it's needed.
"Canada is the friendliest place on earth but on the dartboard we can be mean! We feel pretty confident in each other's games and we'll give it our best shot."
Canada will now face Belgium, who saw off Latvia 2-0 but needed a gritty fightback from Dimitri Van den Bergh against Madars Razma to avoid a doubles decider.
Kim Huybrechts gave Belgium the early advantage with a 4-0 defeat of Janis Mustafejevs, only for Razma to take a 3-1 lead in his clash with Van den Bergh.
The World Matchplay champion survived two missed match darts in leg five as he posted a 14-darter to begin his fightback, before levelling and then taking victory with a 103 checkout.
"We showed we are humans today," said Van den Bergh. "We gave it our best but sometimes it doesn't go the way you want it to and we know we can do a lot better.
"I had to dig deep. I was struggling but I still managed to scrape the win, and I believe in us. I know we will raise our game and tomorrow is a new day."
Austria moved into the quarter-finals for the fourth time in five years by defeating Portugal 2-0 in their second round meeting.
Mensur Suljovic opened the tie with a 4-2 defeat of Jose De Sousa, who hit back from 3-0 down to threaten an upset, before Rowby-John Rodriguez overcame Jose Marques 4-1 to seal the win.
"It's a big win," said Suljovic. "Jose is a brilliant player but today I was better than him, and I was focused.
"Rowby is a great friend and I've known him since he was young. We are a good team and I'm so happy to be through."
England's Michael Smith and Rob Cross ended Lithuania's hopes with a 2-0 victory to book their spot in the quarter-finals against Austria.
Smith averaged 91 as he defeated Darius Labanauskas 4-0 in the opening singles tie - although the Lithuanian had missed his chance to take leg one - before Cross came from 2-1 down to defeat Mindaugas Barauskas 4-2.
Saturday November 7
Afternoon Session (1.30pm local time, 12.30pm BST)
TV Coverage: Sky Sports
Second Round (Best of 3 points)
(Two best-of-7-leg singles matches & one best of 7 doubles decider if required)
Evening Session (7pm local time, 6pm BST)
TV Coverage: Sky Sports
Second Round (Best of 3 points)
(2x best-of-7-leg singles matches & one best-of-7-leg doubles decider if required)
Sunday November 8
Afternoon Session (1pm local time, 12pm BST)
TV Coverage: Sky Sports
Quarter-Finals (Best of 3 points)
(2x best-of-7-leg singles matches & one best-of-7-leg doubles decider if required)
Evening Session (7pm local time, 6pm BST)
Semi-Finals (Best of 3 points)
(2x best-of-7-leg singles matches & one best-of-7-leg doubles decider if required)
Final (Best of 5 points)
(2x best-of-7-leg singles matches, one best-of-7-leg doubles, then reverse singles)