The Northern Irishman, who won the tournament in 2016, chalked up another impressive scalp having already seen off Mark Williams and Gary Wilson as he finished strongest in the first semi-final.
The scores were tied at 3-3 when Allen took control of proceedings, reeling off three frames on the bounce to set up a clash with Zhang Anda or Mark Selby.
Allen edged the first frame thanks to a smart yellow in the bottom left pocket that opened up the table but saw his lead wiped out as Carter hit back. There was little to pick between the pair heading into the mid-session break, Allen notching up a break of 108 in the third only to watch as Carter responded with 106 of his own.
Carter blinked first as he gave up the lead once again with errors in a closely fought fifth frame and, although he was able to level up for the third time, Allen was about to make his move.
He won back-to-back frames for the first time, leaving him one away from victory. The pair took it deep with a series of visits before Allen finally seized the opportunity to clear up, sending the black into the centre-right to wrap things up.
Saturday’s action sees Selby attempt to recreate the form that allowed him to blow away Ronnie O’Sullivan 6-0 in the quarter-finals, with third-seed Zhang standing in his way.
More pain for Higgins
Zhang Anda's dream season continued has he beat childhood hero John Higgins in the last eight of the Players Championship in Telford, eventually winning 6-4.
Zhang – winner of the International Championship earlier in the campaign – completely dominated the early part of the match as he piled on the big breaks, racing into a 5-1 lead before Higgins responded with a typically brave comeback.
Having barely had a look in after taking the opening frame, Higgins suddenly burst into life as his opponent faltered slightly with the winning line in sight, the veteran Scot reeling off three frames on the spin with the aid of 84 and 71 breaks.
With the deficit cut to one, Higgins had a couple of golden chances to force a decider, missing a tricky red with the spider and then later a much more straightforward black of its spot with the frame at his mercy.
It was an achingly familiar story for Higgins who has lost a number of close, high-profile matches in the last 24 months, and this one will sting given a last-four clash with Mark Selby on Saturday night was the prize for the victor.
To his credit, Zhang held himself together really well to finish the job, his 56 clearance overshadowed by earlier breaks of 102, 79, 84, 104 and 95, but arguably more impressive given the circumstances.
Zhang told World Snooker Tour: "I played pretty well, because I wanted to show what I can do in front of my hero.
"I was very dedicated to the job and I was able to concentrate on each shot.
"Even when he was coming back at me, I wasn't feeling nervous and I was very much enjoying watching his performance."
Fast Results
Scores
