Walden, a winner of two ranking titles who had never won a match at the Crucible before last week's 10-1 defeat of Michael Holt, will face Michael White next with the victor to go through to the one-table set up at snooker's theatre of dreams.
Milkins, who shocked Neil Robertson 10-8 in the first round, fought hard to win seven out of nine frames in the middle of the match, but in the end it was Chester's 30-year-old Walden who got to the winning post first.
Trailing 10-6 overnight, rapid potter Milkins got the fast start he needed with breaks of 71 and 76 to win the first two frames tonight in just 17 minutes. Walden was relieved to get the better of frame 19 with a top break of 61 and he started the next with a 55 only for Milkins to battle back and snatch it by clearing from the last red to pink to make it 11-9 at the interval.
Gloucester's Milkins continued his recovery by winning a scrappy 21st frame then Walden went two up with three to play thanks to a run of 79. Walden had two good scoring chances in the next but missed a pink to one centre pocket and a red to the other, and Milkins converted an excellent pot on the third last red on his way to making it 12-11. But when another chance came Walden's way in frame 24 he kept his composure in a decisive break of 86.
"I am delighted to get through because Rob put me under all sorts of pressure tonight," said Walden, who won the Wuxi Classic at the start of this season. "The momentum was with Rob and he was throwing everything at it. I was just battling and trying to keep calm. I thought it was going to go to a decider but thankfully I nicked the last frame.
"If you are in the quarter-finals then you have got a great chance. I am feeling pretty decent out there so I think it is only a matter of who settles better. I am relaxed out there and I am enjoying every moment and hopefully I can keep progressing.
"It is definitely a different experience for me. The tables are lovely and the venue is brilliant. There is no better place to play snooker, it is what you dream of as a child. You need to stay focused but it is hard not to get carried away when you see the draw opening up."
Milkins said: "I played really well this evening but it was a bit too much to catch up. I played well and Ricky did not look like he was twitching at all. He looked like he was going to punish me if he had the chance. He played really well and he held himself really well because I put him under a lot of pressure tonight.
"It has been a great week. I have beaten Neil Robertson and that was a great win. I was more impressed about the way that I played tonight. I really came out and produced some good snooker. Over the match there were a couple of close frames that I lost, it could have been a totally different story if I had potted the last black in the first frame instead of missing it."
