Trump spurned repeated opportunities to win the match, missing a red in the 18th frame with snookers already required, only for Robertson to fight back.
The Australian eventually sealed victory with his fifth century of the match just before 11pm, triumphing in Coventry for the first time since his maiden Champion of Champions victory in 2015 in a final of the highest quality.
"I can't believe we've played a match like that," Robertson said, struggling to hold back the tears before being embraced by his family.
"It's the best match I've ever been involved with. It had everything."
In Trump's case, he found it hard to be disappointed with his performance despite coming out second-best.
"Neil scored the heavier tonight when he needed to and overall he deserved to win," Trump said.
"He played the better snooker over the two sessions.
"I'm not too disappointed. It's always a joy playing Neil because he plays similar to myself and he gets on with it."
Robertson had taken the early lead with a fine break of 112 in the second frame but the match really came to life in the fifth frame.
Trump went on a run of three consecutive centuries, totally 367 unanswered points to turn a 3-1 deficit into a 4-3 lead.
But Robertson is not short of form himself and added 230 points of his own without reply, courtesy of breaks of 96 and 111, to end the afternoon session leading 5-4.
COVENTRY, ENGLAND - NOVEMBER 10: Judd Trump of England plays a shot in the final match against Neil Robertson of Australia during the Champion of Champions 2019 at Ricoh Arena on November 10, 2019 in Coventry, United Kingdom. (Photo by Tai Chengzhe/VCG vi
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The quality on show was high - one of Robertson's century breaks saw him miss the 14th red with a 147 beckoning - and the lead ding-donged between the pair; leading 7-6, Trump tried to snooker Robertson behind the green after 10 minutes of the frame but only succeeded in going in off.
Neither man could take control of the frame though with the reds awkwardly set and Trump anxiously missed with 36 on the board to allow Robertson back to the table.
The Australian levelled but the world No 1 across the table continued to show his tremendous cue power, navigating a tricky table to retake the lead and move to within two frames of the title, leading 8-7.
Trump had a reminder in the very next frame though of the level of the final and what would happen if he left the door ajar: he gave Robertson an opportunity from the break and he capitalised immediately with a break of 135, the seventh century of the match.
He was back at the table immediately afterwards, making 36 before playing safe instead of forcing the pack open, perhaps the first sign of anxiety.
The ensuing safety battle ended with Trump slotting a brilliant long red but with colours almost all safe, break-building was a challenge.
He quickly ran out of position quickly and Robertson got himself back in among the balls, potting frame ball but unable to force the brown in to make a 9-8 lead a certainty.
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Just as Robertson had in the previous frame, Trump put his opponent through the ringer but unlike the previous exchange, he succeeded, forcing him to miss the blue ball and moving back within striking distance.
Eventually, Trump earned the chance to pot the blue, sinking a nerveless long blue down the side cushion, played at dead weight, to set up a clearance of the last two balls.
Just one frame way from defeat, Robertson appeared untroubled by nerves and sunk a long red with his first shot into the very centre of the pocket.
But he then missed a difficult but not impossible pink into the corner and Trump went to work, strutting around the table on his way to, surely, a century that would seal the title.
But there was one more twist left in this marvellous final, as he sunk frame ball but missed the next, and Robertson was not going down without a fight.
Knowing that one four-point snooker would allow him to tie the frame, Robertson went down to the final red before putting Trump behind the black and picking up the four points he needed.
Robertson duly forced the re-spotted black with a clearance and Trump was cavalier in his approach, leaving his opponent a simple chance to force the decider, which he won in one visit of the highest quality with a break of 137.