Higgins could and probably should have won, but could not finish off the match as his profligacy came back to haunt him just before midnight on Thursday at a London venue brimming with tension.
The four-times world champion managed to scramble 57 points clear in the final frame only for Selby to recover aided by some terrific tactical play and his opponent's mysterious inability to finish matters off.
Both men had chances to seize the initiative in the final frame, but Selby secured a meeting with Shaun Murphy in Saturday's first semi-final when he doubled a blue to the right centre pocket before clipping in a pink to the same bag.
A gloomy Higgins had no excuses for the defeat having squandered numerous opportunities to progress, but can console himself with the knowledge that he contributed to a classic evening's entertainment at the game's biggest invitational event.
"I bottled it," he said.
Selby appeared to endorse such a feeling after maintaining his perfect record in final-frame deciders at the Masters. Astonishingly, the three-times winner has now won all 10 he has contest at the tournament.
"John didn't play near his best. He was there for the taking, but I found myself 5-3 down," said Selby.
"I felt I was going out of the tournament, but I thought I might as well go out fighting.
"I thought I'd play the double on the blue, and thankfully I dropped in the pink. I was confident going into the final frame. I didn't fancy it at 5-3 down because John was playing better than me. He missed a brown at 5-4 by a long way.
"I knew then he was under pressure, and I could get through.
"Shaun is another tough match. He seems to be striking the ball so well again, and probably should have done more in the sport than he has.
"Now I need a day off I think to recover from that."
Higgins thumped a long red into a top pocket as he contributed 58 in the opening frame before an error by Selby enabled the Scot to return to the table to secure a 1-0 advantage.
Higgins had chances in the next two frames, but a few untimely mistakes - including a bad miss on a red among the balls in frame three - saw Selby make 42 and 70 in moving 2-1 clear.
Higgins could not be blamed for feeling slightly disenchanted as a knock of 98 carried Selby 3-1 ahead at the mid-session interval.
It was Selby's turn to squander an obvious chance in the fifth frame as a missed red to a centre pocket provided Higgins with scope to run in 43 to help him trail 3-2.
That quickly became 3-3 as Higgins made 69 by displaying the level of form that brought him two Masters titles in 1999 and 2006.
Selby looked favourite to restore his lead at 4-3 with a 56, but Higgins relied on his trademark matchplay skills to battle back into the frame before winning it on the black bolstered by some reliable safety play on the final ball.
Higgins pieced together 42 in the eighth frame, but a missed blue proved to be the pivotal moment as a couple of well-placed snookers saw the tactically sound Higgins snare his fourth straight frame.
He was presented with the opportunity to win frame and match after Selby had contributed 48 in frame nine, but losing the cue ball saw him miss a tricky red as the Leicester player extended his stay at this year's tournament with a fluent 61.
Higgins opened up the 10th frame with 37 only for Selby to respond with 42 as it came down to a safety joust on the final red.
Higgins had chances to seal the win, but he got a kick on a green before missing the brown by some distance at pace as Selby held his nerve by running in the final pink to level at 5-5 before edging that 38-minute final frame.
He punched the air in delight. He could not be blamed.