Higgins - world champion in 1998, 2007, 2009 and 2011 - strangely does not have the best of records at the invitational tournament despite winning it twice in 1999 and 2006 with a string of losses in the first round blighting his record.
He looked likely to endure another afternoon of hardship after falling behind early on against the two-time world championship finalist Carter.
Scotsman Higgins somehow contrived to lose the opening frame of the afternoon when he missed a simple black along the top cushion to leave Carter needing a snooker having made 59 and holding a 63-0 lead.
His opponent cut a composed figure in controlling the white ball to some effect in mopping up with a 64 to pinch the frame by a solitary point.
Carter somehow managed to snatch the second frame after gleaning the two snookers he required on the colours as Higgins hit the pink attempting to nudge the brown before missing the brown as he swerved past the black.
Higgins fluked a snooker behind the blue seconds later, but watched as Carter managed to escape from the snooker and hole the brown.
With tension mounting, Carter held himself together to claim the frame with a cool pot on a black from distance after both men had failed to sink the black.
Carter was first among the balls in the third frame of the day, but missing a red on 21 proved fatal as Higgins showed his class with a run of 117 ensuring him of his first frame of the day.
Breaks of 44 and 46 saw Higgins head for his cup of tea at the mid-session interval level at 2-2 when he could easily have led 4-0.
Carter was left spectating in the fifth frame as he failed to pot a ball with Higgins dominant in constructing a 3-2 advantage.
Carter had gone over 40 minutes without potting a ball and his anxiety was illustrated by an attempt at a long red that was hit too hard in the sixth frame.
Higgins stepped in with a 97 to snare his fourth straight frame for a 4-2 lead.
He looked on the cusp of a 5-2 advantage having erected a 38-0 lead, but a red eluded him to a middle bag when he seemed set for another heavy contribution.
Carter potted his first ball in just under an hour before proceeding to make 83 to half the bleeding and trail 4-3.
The eighth frame was far from memorable, but Higgins emerged on the right side of several safety duels to establish a 5-3 lead.
He completed the win when Carter broke down on 54 as a couple of misses on reds to a middle pocket proved fatal.
Higgins cleared with a 65 to finish matters off.
He will face last year's Masters finalist Shaun Murphy or Ricky Walden in the last eight and was content to keep alive his pursuit of a third Masters title.
"I could have lost 6-0 or been a 6-1 loser after losing the first two frames so I was just trying to stay positive. I've never had the best of records at this tournament as a professional," said Higgins.
"I'm happy to be through. It is seven years since I played Ronnie (O'Sullivan) in the final. I still remember it. I'm a bit fatter with a few more grey hairs as years of playing snooker take their toll.
"The crowd were very good today, and I still think this venue is better than the Wembley Arena." Carter, watched by former world champion and friend Peter Ebdon, was not feeling in peak condition due to his ongoing struggles with Crohn's disease.
He is not overly concerned with his form, despite losing after collecting the first two frames. Carter has hinted at retirement in previous years.
"I'm disappointed. A 2-0 lead is still early days against John. I'm naturally disappointed, but I don't really target this tournament. It is just a tournament I have never really done well in.
"I'm not in the best of conditions healthwise. That is a work in progress really. But I'm looking forward to the rest of the season."
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