The 30-year-old will face Barry Hawkins in a repeat of the 2018 Paul Hunter Classic final at the same venue, when Wilson emerged victorious.
Wilson established a 4-2 lead only to be pegged back by breaks of 73 and 69 from his opponent.
Carter took the lead for the first time since the first frame to make it 5-4, but it needed a run of 53 from Wilson at the start of the decider to eventually clinch victory.
"Ali turned it on from 4-2. You can't afford to let him off the hook," Wilson said in his post-match interview.
"I was pleased with how I responded at 5-4 down. I made two good breaks and kept the pressure on."
Hawkins swept aside Mark Williams 6-2 to book his place in Sunday's best-of-17 frame final with a first prize of £80,000.