Walden came up with a lovely clearance of 86 in the 24th frame after Milkins had made a mess of a positional shot. It was more than enough to secure his progress to a meeting with Michael White in the last eight.
Walden's win means half of the quarter-finalists at the Crucible are making their debut at this stage of the tournament with White, Stuart Bingham and Barry Hawkins the others.
Milkins had ousted 2010 winner Neil Robertson in the first round, and looked like he could have recovered from 10-6 after making a sprightly start to the third session.
Knocks of 71 and 76 carried the Gloucester player back to 10-8 behind in less than 20 minutes before Walden steadied himself with 61 helping him move 11-8 clear despite suffering the effects of a huge kick when trying to hole a red.
Walden was first at the table in the 20th frame, but a run of 55 was not enough as Milkins recovered to pinch the frame on the black.
He dominated the 21st frame to close to 11-10 behind, but Walden showed the form that saw him win the Wuxi Classic in China last summer as a 79 carried him to the cusp of victory.
A brave pot on a red to a middle bag helped world number 19 Milkins close to 12-11 behind, but Walden prevented the match from going to a deciding frame with a clinical break in the 24th frame.
He is guaranteed £24,000 for reaching the last eight, but will surely be keen to progress to the one-table situation at the Crucible against promising Welsh kid Michael White, who is world number 41 and unproven at such a late stage of any ranking tournament, never mind the World Championship.
SECOND SESSION REPORT
Ricky Walden took a 10-6 lead over Robert Milkins following the second session of their World Championship second round match at the Crucible.
Walden rattled off the first four frames of the evening session to lead 9-3 at the mid-session interval to leave himself with the chance of securing his place in the quarter-finals with a session to spare.
However, Milkins won the next three frames to cut the arrears to 9-6 before Walden replied with a break of 51 in the final frame to take an over-night lead of 10-6.
Milkins had signed off from their morning session with a 104 break, but he struggled for any form of fluency when play resumed for the evening session as Walden won the first two frames - which were both scrappy affairs - 54-13 and 75-14 to extend his lead to 7-3.
Breaks of 63 and 76 followed as Walden opened up a six frame advantage at the mid-session interval, as Milkins’ break building and safety play left a lot to be desired.
A rally after the interval saw ‘the Milkman’ cut the arrears to 9-6 but Walden prevailed in the final frame to retain both the momentum and upper-hand going into their final deciding session.
The winner will play Michael White, who beat Mark Williams in the opening round then disposed of Thai Dechawat Poomjaeng easily in round two.
FIRST SESSION REPORT
In a session which featured few large breaks but was entertaining nonetheless, Walden opened up a 3-0 advantage.
After Milkins racked up a 106 break ahead of the interval they alternated in winning frames - with a 104 clearance from the Gloucester 'Milkman' ending the session - to leave the match wide open.
This is the first time in eight years that Milkins has reached the Crucible, disposing of six-times finalist Jimmy White 10-5 in the final qualifying round. He then ousted 2010 champion Neil Robertson 10-8, having trailed 5-2, in the first round. Despite his centuries, he struggled to replicate that form for long periods against Walden, failing to make another half-century.
There was black-ball drama as early as the first frame. Walden should have put it to bed but missed the black off its spot with his opening break at 60. Milkins needed to clear the table and almost did so - leaving the black over the pocket for his grateful opponent to knock in.
Wilkins dominated the second frame with two decent scoring visits, Milkins miscuing on a brown in between, and a 76 break for the Chester cueman then proved enough to extend his lead still further. Milkins responded in style with that century, and the match was fairly even from there.
After the mid-session interval Walden went 4-1 up with a 64 clearance to the pink. He then came back to 47-47 in frame six before putting the white and yellow on opposite cushions: Milkins missed down the length of the table while trying to feather the yellow then caught it too fully on his next try. However Walden missed his half-chance of a pot and his opponent claimed the frame to reduce the arrears.
The score was soon 5-2 as Walden's smooth break-building saw him home but Milkins boosted his chances in the match - and his confidence - with a brilliant 104 clearance.
Walden has two ranking wins to his name, including this season's Wuxi Classic - where he beat Milkins in the last eight.