The “Captain”, making his twelfth appearance in the prestigious invitational event, reached the semi-finals in London for the first time in his career with a hard-fought victory over the Scot.
However, there was a huge talking point late in the game when the tie was still delicately poised and likely to go either way.
Leading 4-3 and midway through a vital eighth frame, Carter attempted a straightforward safety on the yellow.
Referee Desislava Bozhilova called a foul and a miss only for the Englishman to immediately insist that he had connected with the object ball.
The decision was reversed and the players continued, but replays confirmed that Carter had indeed missed the yellow and the foul should have stood.
In commentary for the BBC, John Virgo was particularly incensed, saying: “I don’t care, if the referee says he didn’t hit it, then he didn’t it. (She) should be stronger.”
It is debatable whether or not the incident had a significant influence on the outcome of the frame.
As it was, Carter won it to move 5-3 in front before sealing his place in the last four with a break of 72 – his only contribution above 50.
In his post-match press conference, Carter said: “If I haven’t hit that then I’m absolutely flabbergasted because I don’t know what’s happened there.”
“I was playing it full ball, the white’s going up the table, and it’s turned…anyone would tell you that I’d never try and gain an advantage doing that. That’s unbelievable.”
Carter, ranked 17th in the world rankings, only received an invite after Ronnie O’Sullivan’s decision to not enter this year’s edition.
The 40 year-old will meet Shaun Murphy in the next round after the 2015 champion beat Joe Perry by the same scoreline.
Stephen Maguire faces David Gilbert and Stuart Bingham entertains Kyren Wilson in the remaining two quarter-final fixtures on Friday.