Higgins – a two-time UK Championship titleholder – quickly took a 4-1 lead in York with two breaks of 70, a 78, and a 60.
The Scot had a chance to extend his lead in the sixth frame, but some sloppy potting allowed Murphy to get back into the match.
At 5-3, Higgins was one frame away from victory until Murphy produced breaks of 89 and 53 to force a deciding frame.
Both players had opportunities to clinch the match, but a crucial miss by Higgins on the yellow gave Murphy the chance to clear the table and prepare for a quarter-final against Zhang Anda.
"It's the classic saying of taking it one ball at a time," Murphy told the BBC.
"Whenever you face anyone from the Class of '92, you have to be at your best, and any victory is worth celebrating. Especially coming from that position, this ranks as one of my greatest wins."
Hawkins delivers a whitewash over Slessor
Last year's runner-up Barry Hawkins easily defeated Elliott Slessor, cruising to a 6-0 whitewash to set up a clash with Mark Selby.
The 46-year-old Hawkins compiled breaks of 94 and 87 to establish a 3-0 lead, giving him control of the match.
He narrowly took the fourth and fifth frames from Slessor to move close to victory as his opponent looked puzzled in his seat.
He sealed the win with a commanding 73 break, finishing the match with a dominant 491-143 points margin.
Friday afternoon’s session features reigning champion Judd Trump against Ding Junhui , while three-time UK Championship winner Neil Robertson faces Pang Junxu.
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