The Australian had led 8-6, but Perry then grabbed the momentum by taking three frames in row - the third of them with a break of 93 - to edge 9-8 ahead and put himself on the verge of a first ever ranking title.
Robertson responded, however, with a break of 87 to force a decider in which it was Perry whose reserves of nerve and luck failed.
The 39-year-old, playing only the second ranking tournament final of his career (and his first since the 2001 European Open), got the first chance in the 19th frame, only to run out of position after scoring just 14.
Robertson stepped in with a break of 78, claiming both the frame and the match to record the 10th ranking title of his career, and with it the £85,000 first prize.
Perry had looked in control of the match early on, winning the first three frames and recording a break of 135 in the sixth to go 4-2 ahead.
Robertson then found his touch, winning six of the next eight frames to take an 8-6 lead, before Perry sparked to life with his late run of three frames on the bounce - one of which he claimed on the black.
But he could not sustain it, and Robertson stepped up to win the opening tournament of the 2014-15 season.
The snooker tour now moves to Bendigo for the Australian Goldfields Open, which begins on Monday.