Despite a maximum break of 147, the Scot trailed 7-2 after the opening session.
But breaks of 89, 74, 76 and 71 helped Higgins win six frames in a row.
Trump levelled at 8-8 with a break of 105, a third century of the match for the Bristol cueman who roared into a 5-0 lead via breaks of 112, 80, 74, 111 and 59.
The 23-year-old drew level once more at 9-9 but a run of 61 saw the four-time world champion take the decider.
It is the 25th ranking title of Higgins's career and the first since he beat Trump in the final of the 2011 World Championship.
The world number three takes home the championship trophy, 7000 ranking point, a winners’ cheque for £75,000, plus an extra £12,000 for recording a maximum break.
Higgins' 147 in frame six was just the fourth in a ranking final and the 91st maximum in snooker history.
Runs of 51 and 53 from Trump, sandwiched by 51 from Higgins, saw the Englishman take a five-frame lead into the evening session but that was not enough in a final of incredible quality.
"To beat Judd from 7-2 down is unbelievable, I can't explain how it feels because I'm shell-shocked," said Higgins. "In the first session he steam-rollered me, but I still felt confident that if I came back tonight and played my best I would have a small chance. To beat Judd when he was playing that well must be one of my best wins ever," said Higgins of his win.
"I could have won 10-8 but I started feeling some pressure and played a bad shot from brown to blue, that was just nerves. In the last frame I decided to go for the long red full-blooded and luckily it went in. To clear up was a great feeling.
"It's a big loss for Judd to take. He'll have defeats like this in his career - we all do - and he'll win a lot of titles. If you can come back stronger from them, that's what defines the great champions. He's a flair player in the mould of Alex Higgins, Jimmy White and Ronnie O'Sullivan and he's great for the game."
Trump was magnanimous defeat: "John's the best I've ever played against. He played so well tonight and didn't give me a look-in until it was 7-7. In the last frame I was a bit unlucky not to get on the black. He took on a risky red, potted it and did well to clear up.
"Going into tonight I knew John was a great battler. I've played him before and been well in front and he's come back at me. The 147 showed what a class player he is but it only wins one frame and I won the next one so it didn't have any impact."
- Alex Higgins