The four-times world champion has cut a troubled figure in recent times in trying to find some consistency using several new cues to enhance his game, but always looked the likelier player against a strangely subdued Bingham at London's Alexandra Palace.
His reward is a match with defending Masters champion Mark Selby, who edged Mark Davis 6-5 earlier on Sunday.
With five Masters titles between Higgins and Selby, that should make for an engrossing quarter-final on Thursday evening.
The Scotsman - winner of the Masters in 1999 and 2006 - has done little or nothing of note since losing 10-7 to Neil Robertson in the Wuxi Classic final in China last June having won the Bulgarian Open with a 4-1 win over Robertson a fortnight earlier.
"I've played better than I've played in the past few months," said Higgins. "Stuart didn't play well at all. I didn't expect him to miss some of the balls he missed.
"I was in the depths of despair after losing to Stephen (Maguire) at the UK Championship last month. I basically threw the old cue away. My mate Raymond back in Scotland made me four new cues, and I picked up this one right away.
"I feel a lot more confident playing with this cue than I have been in the past few months so it is a start for me.
Higgins added: "You can only tell you what your inside is telling you. I was basically in turmoil the past few months, and didn't know where I was going. I practiced hard over Christmas, and I felt my tempo was a lot better around the table.
"It is heartbreaking when your tempo is not up, but it is different when you are happy and making breaks. It is a big positive for me.
"We've only been here twice, but this is a lot better than the Wembley Arena. I felt that was a soulless venue. This is a lot better.
"My brother is flying down from London for a few days so I'll practice and spend a couple of nights with him before he goes back up the road on Wednesday. He probably thought I'd lose again and he'd miss me...
"I feel I can give Mark a game, even though I'll be the underdog again."
Breaks of 50, 94, 65 and 109 helped carry Higgins to the cusp of a place in the quarter-finals here and a 5-1 advantage before Bingham sprung to life with a 91 in the seventh frame.
Higgins had picked up a scrappy opening frame, and should have moved 2-0 ahead, but was let down by a poor positional shot in trying to land on the pink from blue.
Higgins missed a tough cut on the final black moments later that would have finally sealed the frame. Bingham potted black before a loose safety shot enabled Bingham to level at 1-1 by repeating the dosage on the re-spotted black.
His opponent would not be deterred as several errors by Bingham saw Higgins snare the next four frames with minimal fuss.
He finally secured his place in the last eight when Bingham played one sloppy safety shot too many in the eighth frame.
Bingham has never been beyond the first round of the Masters. The Basildon man was disappointed having overcome Ronnie O'Sullivan in the UK Championship last eight last month before losing 9-8 to Neil Robertson in an epic semi-final.
"It is disappointing, but you don't deserve to win when you play like that," said Bingham. "It was comical stuff with three and four chances a frame. John didn't need to be at his best to beat me."
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