The Scot moved 7-2 ahead thanks to a break of 72, putting him within two frames of victory and leaving Carter looking down the barrel of a heavy defeat. But Carter fought back bravely with a break of 60 to reduce the deficit before winning an astonishing 11th frame.
Higgins opened with a break of 72 only for Carter to complete a clearance of 73 to clinch the frame and make it 7-4. But Higgins extinguished any hopes of a fightback as he took the next frame with a break of 40, but only after being given a scare when Carter's first attempted pot saw a red rattle in the jaws of the middle pocket before rebounding across the table into the opposite pocket.
Carter eventually made 36 but Higgins came through a tense safety battle to prevail.