The encounter on Saturday opened in even fashion as both players exchanged half-centuries, until Robertson produced a superb 114.
Robertson seized control by consolidating with the fifth frame to move 3-2 up and played the crowd by mimicking cricket strokes in a nod to his Australia closing in on a 2-0 lead in the Ashes.
But this Australian couldn't press on as Trump surged back, winning four straight frames on the back of half-centuries.
A last break of 53 confirmed his place in a fifth career UK Championship final and a chance to retain his crown.
"Another final," Trump reflected afterwards. "So it's been a good end to this calendar year, really, after quite a poor midseason. I'm happy to have another shot at it.
"It's not been brilliant the whole tournament. I'd love to play better, but at the moment I haven't really needed to."
Awaiting Trump in Sunday's final will be one of Mark Selby or Shaun Murphy, who take on Saturday's second semi-final at 19:00 GMT.