He will face Jack Lisowski in the last four on Saturday after the Cheltenham player punished an awful Judd Trump error on his way to completing a 6-2 victory over his close friend in Thursday's opening quarter-final.
World number five Trump - winner of this tournament in 2012 with a 10-8 success against Robertson - looked certain to close to 4-3 behind leading 57-27 in the seventh frame, but he missed a simple red down the cushion on a break of 57 that would have left Lisowski needing a snooker.
Allen beats Robertson in phenomenally high-standard final
Lisowski produced a composed clearance, including a wonderful pressure blue, to pinch the frame by three points on the black before an exquisite break of 106 ensured his progress to the last four.
Selby and Robertson were locked at 7-7 apiece in career meetings before their latest riveting encounter.
The pair turned professional two decades ago - Robertson in 1998 and Selby a year later - and both former world champions were close to their best form before an enchanted crowd.
World number one and defending champion Selby - bidding for a third straight win here to go with his titles in 2016 and 2017 - made a blistering 137 break in the opening frame only for Robertson to roar back by claiming the next two frames for a 2-1 lead that saw him roll in a quite magnificent 135 in the third frame.
A sturdy 83 from Selby restored parity at the mid-session interval at 2-2 before the Leicester player dominated the next two frames with Robertson failing to pot a ball.
A 133 knock in the sixth frame was simply majestic from Selby, but the 2012 runner-up Robertson was far from finished as he scrambled over the line in the seventh frame inspired by an unbelievable make-or-break pot on a long red trailing 33-45 and facing a 5-2 deficit.
Selby makes plant from snooker heaven
That appeared to give Robertson a major confidence boost as he next pieced together a quickfire 113 to bring the match centuries to four and the scoreline level at 4-4.
With the tension palpable as the match suddenly became a nail-biting best-of-three shootout, Robertson gained an early 24-9 lead amid a bout of superb old school safety play before a Selby error attempting a long red proved fatal.
The Melbourne man was firmly in the groove to move one up with a possible two frames play as he pieced together a pristine 95 for a 5-4 advantage. And he closed out the match to set up a meeting with Lisowski in the last four courtesy of a timely 53.
The world number 21 Lisowski continues to search for his first major title having lost the Riga Masters final to Robertson in July.
But 'Jackpot' will hope to hit the jackpot in his eighth year as a professional knowing a top prize of £175,000 awaits the champion.
Trump's 'incredible' miss costs him key frame on his way to defeat
He benefited from one of the most outrageous flukes you are likely to see on a snooker table early in the seventh frame, but in truth was always the likelier figure with breaks of 53, 95 and 71 helping him open up a 3-0 lead before a 52 and 119 saw Bristol's Trump close to 4-2 behind.
Masters champion Mark Allen overwhelmed two-times World Championship finalist Ali Carter 6-0 in the other completed quarter-final boosted by breaks of 70, 57 and 129.
Allen will meet the rejuvenated Welshman Matthew Stevens, who upset China's leading player Ding Junhui 6-5 in the last 16 on Wednesday to reach the quarter-finals of a ranking tournament for the first time since 2014.
He edged out Martin O'Donnell in a last-frame decider to secure a meeting with the Northern Irishman over the best-of-19 frames on Friday.
INTERNATIONAL CHAMPIONSHIP QUARTER-FINALS
- Jack Lisowski 6-2 Judd Trump
- Mark Selby 4-6 Neil Robertson
- Martin O'Donnell 5-6 Matthew Stevens
- Mark Allen 6-0 Ali Carter
Watch Roberton's lovely double against Lisowski
Watch Roberton finish off classy century break to stretch lead over Lisowski