Murphy, seeded sixth, failed to get a point on the board in three frames, with 10th seed Higgins putting together a stylish break of 138 to take the fifth.
Fifth seed Neil Robertson was almost as convincing in his victory over Graeme Dott, easing to a 6-1 success.
The Australian raced into a 3-0 lead, posting breaks of 67 and 56 in the opening two frames, and although Dott took the fourth, a narrow 60-57 win in frame five proved pivotal and Robertson never looked back.
An upset looked to be on the cards when 17-year-old Zhou Yuelong took a 4-2 lead against Thailand’s Thepchaiya Un-Nooh.
Yuelong seemed well in control when putting together a frame-winning break of 115 in the sixth, but Un-Nooh hit back to win 6-5 and make it through to the last eight for the second tournament running.
It was another close contest in the fourth game of the morning session as Joe Perry held off a late charge from Ben Woollaston to claim a 6-5 success.
Woollaston came from 5-2 down to make it 5-5 and force a decider which turned out to be a one-sided affair as Perry found his form to squeeze through.