Carter's hopes looked slim when he went three down with four to play, but the 2008 runner-up pulled victory out of the hat to set up a quarter-final with Jamie Jones or Andrew Higginson (Phil Haigh writes).
It was looking like a miserable season for Carter after a poor run of results and a flare up of his Crohn's disease. But a new dairy and wheat free diet has made the difference on and off the table and he can afford to start dreaming of another appearance in the final at snooker's Theatre of Dreams.
Trump won the UK Championship in December but has failed to add to his tally of titles in the second half of the season and finishes the campaign disappointed to miss out on the chance to repeat his heroics of 12 months ago.
A half-century from Trump was enough for him to claim the opening frame of the day, but Carter responded in kind with a break of 70 to leave the score at 10-8. There was some serious excitement building in the crowd in the next as Trump sank 12 reds and 12 blacks, looking good for a maximum, but he just ran out of position having made 96, but it was enough to take the frame.
The Captain responded with a 94 of his own to stay in touch, but when Trump took the 21st frame it looked like he had done enough, leaving Carter needing to win the last four.
Carter was on for a maximum himself though in the next, missing on 81, but it was the start of an incredible comeback. He added the next two with a top run of 53 to make it 12-12.
Trump had two clear chances early in the decider, but missed a mid-range red to a corner, then another red to the other top corner with the long rest. Carter made a calm 47 to go 48 points ahead with one red left.
Trump battled on and got three of the four snookers he needed as the tension mounted, but Carter finally potted the last red to secure his progress.
"I knew I was hitting the ball well, at 12-9 I thought just get to 12-10 and he knows I'm there," said Carter.
"I played some solid match snooker at 12-11 and that's all it takes. Judd just pots them from everywhere but there's more to this game than just potting them from everywhere believe me, and I've proved that today.
"It's easy for me to say now because I've come out the winner but I'm just delighted with myself because I've been on too many wrong ends of matches like that.
"Now he can feel what it feels like to have a nasty scar in your career. He was in it to win it but so am I."
Trump was magnanimous in defeat, but did suggest that his food poisoning earlier in the week was a factor in his unexpected loss.
"If I was fully fit then I would expect to play a lot better but I just tried to play the best I could in the conditions. He played better, he was more mentally ready and I struggled," he said.
"As soon as I get into the new season then it will be completely forgotten. I'll just go out and play my own game again and hopefully I'll have a better season next year."
Ball by ball scoring and results from tournaments