Scotland will meet China A or Hong Kong in the semis on Sunday, with the final to be played later the same day. The champions will share a cheque for $200,000.
Higgins and Maguire reached the final in 2015, losing to China, and will hope to go one better this time.
They lost the opening frame today then took three in a row to lead 3-1. Williams made a break of 66, the highest of the match, to win frame five, then Wales took a tight doubles frame to make it 3-3.
Maguire and Day were nominated to contest the decider, and it was Maguire who dominated with runs of 59 and 23.
Zhou Yuelong won the World Cup for China alongside Yan Bingtao in 2015
China’s B team of Zhou Yuelong and Liang Wenbo booked their semi-final place with a 4-2 win over Belgian duo Luca Brecel and Ben Mertens. They will now meet England or Thailand.
Brecel took the opening frame for Belgium with a break of 61 before Zhou levelled, helped by a run of 50. China took the next two frames, and despite a run of 78 from Brecel which gave Belgium the fifth to make it 3-2, the sixth went China’s way to seal the result.