Trump, 35, made breaks of 67 and 72 to open up a 3-0 lead but Murphy pulled one back before the interval.
The pair exchanged the next four frames as Trump took a 5-3 lead, but Murphy then made breaks of 78 and 60 in consecutive frames to draw level and set up a decider.
The tense finale came down to the green, which Trump despatched, followed by the brown to leave Murphy needing two snookers.
The 42-year-old successfully snookered Trump once, but ultimately fell short as the latter reached his 46th ranking event final.
“It is a sickener,” said Murphy.
“Once you get to this stage of an event, with such prize money and prestige, you think about winning. Lady luck wasn’t on my side for the majority, but Judd’s ability to keep potting balls is incredible. I think he is the best out-and-out potter we have ever seen.”
Trump added: “I got over the line in the end with a bit of drama. That was a very tough semi-final, but hopefully it wont impact me in the final.”
With a £500,000 prize for the winner, Saturday’s final is the most lucrative match in snooker outside of the World Championship.