The seventh seed, Roland Scholten, beat fellow Dutchman Co Stompe 3-2 and will meet Baxter in the quarter-finals tomorrow evening.
Baxter, the No2 seed from Lancashire, has won almost every worthwhile title in the game but has rarely done himself justice at the Embassy, and last night's victory took him into the last eight for only the second time since he made his championship debut in 1991.
Baxter is determined that this year will be different. "If I play like I did tonight I could go all the way this year," he said. "I was hitting the trebles and then the doubles against Kevin for most of the match. It put more pressure on him as the game went on, but it was never easy."
Scholten was almost down and out against Stompe when he trailed by two sets to one and then lost the first two legs in the fourth set. But he stormed back to win six of the next seven legs to take the fourth set 3-2 and the fifth 3-1.