Trump, the 2019 world champion, struggled in the early exchanges and was 4-1 and 5-2 down in the best-of-11 clash, but stormed back to win four frames in a row to stun Higgins.
The world number five is now favourite to win the tournament after superb breaks of 88 and 111 - his fifth century of the competition - blew his 48-year-old opponent away.
"I went for my long shots and they were going in... I split the pack and it kept happening," Trump told Eurosport.
"It is easy to do it when the pressure is off, but to do it again in the final frame that is when you are proud of yourself.
"I told my brother in the interval that I was feeling tense, and I said I was going to go for it and he told me that is when I play my best."
"I have been hit with a truck there," Higgins added. "He just started knocking them in.
"There have been times before when I’ve missed a few balls, but you have to take your hat off for the way he has done it. He was smashing them in off the lampshades.
"At the end, I did not get a sniff. He was flying. He blitzed me at the end, I have no complaints."
Trump will play the winner of Liu Hongyu and Zhang Anda in Sunday's final.
