The 22-year-old was unable to get away from Neil Robertson in the first session despite breaks of 51, 84 and 67, but opened up a 7-5 advantage in the second.
However, Australian Robertson showed his fighting qualities to level matters before a half-century break gave Trump the edge, and he held his nerve in a tight final frame.
“I think Neil tried to slow it down and make things awkward for me,” said Trump.
“The game went really slow and nothing happened for about 20 minutes and I was just sitting there falling asleep. He came back to 7-7 and I thought he could win from there.
“In the end I think we were over-trying and that’s why we started to miss a few. It’d be nice to end the year on a high and win this tournament.”
Trump will now take on the winner of Saturday’s semi-final between Northern Ireland’s Mark Allen and England’s Ricky Walden on Sunday.
Derby's decision to postpone Sunday's home Sky Bet Championship game against Cardiff was made independently, Derbyshire Police have confirmed.
Rochdale have no new injury worries ahead of Tuesday's Sky Bet League One relegation battle with fellow strugglers Fleetwood.