A tense opening frame set up what turned out to be a thrilling match-up, with Williams taking the lead after a 69-17 win.
But the former world No.1 began to stamp his authority on the match in the second frame, doubling his lead after hitting a 103.
Walden knocked in a 60 to momentarily half the deficit, but back-to-back centuries took Williams clear at 4-1.
The 39-year-old Walden again battled back in the sixth frame with a break of 123, but Williams looked convincing again in the seventh as he moved one away from victory.
However, with nothing to lose, Walden began to find rhythm and successive half-century breaks helped him back to 5-4, and his momentum helped him through a closely-competed 10th frame to set up a decider.
The deciding frame continued to provide drama as Walden enjoyed a storming start, only to let Williams back in.
However, the Welshman then agonisingly missed a red when a clearance would have seen him win by a single point.
Walden made no mistake of sinking the red, capping off a remarkable comeback.
The Englishman will now face either Yan Bingtao and Barry Hawkins in the semi-finals on Friday.