Higgins – a two-time UK Championship winner – raced into a 4-1 lead in York on the back of two breaks of 70, a 78 and a 60.
The Scot could have extended his advantage in the sixth frame, but some loose potting allowed Murphy back in.
At 5-3, Higgins had been within one frame of victory until Murphy pulled out breaks of 89 and 53 to force a decider.
Both had chances to win, but a costly miss from Higgins on the yellow let Murphy clean up and prepare for a last-eight clash against Zhang Anda.
"It's the old cliche of one ball at a time," Murphy told the BBC.
"Any time you play any of the Class of '92, you need your best and any win has to be celebrated. Particularly from that position, it is one of the best wins of my life."
Hawkins whitewashes Slessor
Last year's finalist Barry Hawkins made light work of his match with Elliott Slessor, running away with a 6-0 whitewash to set up a meeting with Mark Selby.
The 46-year-old Hawkins knocked in breaks of 94 and 87 to open up a 3-0 lead, which gave him the upper hand to take full control of proceedings.
He pinched the fourth and a close fifth frame from Slessor to move on the cusp of progression as his opponent was left quizzical in his chair.
He achieved just that with a final ruthless 73 break, completing the rout and leaving with a lopsided 491-143 points advantage.
Friday's afternoon session sees reigning champion Judd Trump take on Ding Junhui while three-time UK Championship winner Neil Robertson plays Pang Junxu.