Selby had opened the final with a 130, having made the 100th official maximum in beating Ricky Walden 9-5 in the semi-finals on Saturday, and moved into a commanding 5-1 lead.
But Robertson crucially took the last two frames of the afternoon session and back-to-back centuries brought him level at 6-6.
He won the next two frames as well and pinched the 16th on the black to move within a frame of victory, which he completed with a 57 break.
Robertson said: “When I beat John Higgins earlier this year in the Wuxi Classic, I said that was the best I’d ever played in a final but the second session tonight was definitely the best I’ve played in a final.”
And, after appearing to wipe away tears, he added: “To become the first overseas player to win all three – Ding Junhui and I basically turned pro at the same time 10 years ago – to get it ahead of him is a fantastic achievement. I’m sure he’ll get there some day as well but to be the first is a fantastic feeling.”
