But the 26-year Englishman cut the deficit to a single frame before running out of steam, with Allen clinching the two frames required before celebrating with a fist pump.
He will face Kyren Wilson, who beat two-times champion Mark Williams 6-1 on Thursday evening.
A 73 from the Antrim native followed up by a sizzling 119 - the first century of the match - and another 50 finally powered the 35-year-old up 8-5 as Wilson's errors proved costly.
The world number 14, who coasted past twice former Masters victor Mark Williams 6-1 in their quarter-final, looked to be heading out as Trump took control with four half-century breaks to move within one frame of victory.
The final first session began in nervy fashion as both players had reached their first Triple Crown Major, with Allen on route defeating Ronnie O'Sullivan, John Higgins and Luca Brecel.
"I went into Pizza Express at the interval and people came up to me wanting signatures - that's what I want".
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Astonishingly, the world number three Trump would only score 28 more points in the final four frames as knocks of 57, 107 and 72 proved enough for 2015 Shanghai Masters victor Wilson - ranked at 14 in the world - to reach the final of the sport's biggest invitational event.
That break was the highest of the match at that point but Wilson quickly bettered it by three to take the next frame before Allen pegged him back by grinding out the next one.
Speaking in his post-match press conference, Allen admitted to feeling slightly overcome by the occasion during the afternoon session before easing himself into the encounter. You're never going to win one of these triple crown events easily and that was the test, it would have been easy to crumble.
"It means so much to me", he said. I was completely shitting myself in the first session.
The ringing mobile went off three times before the hapless spectator was escorted from the arena but Wilson, who was forced to get up off his shot each time, showed no ill-will and asked for the man to be let back in.
"I'm just very pleased and to be on the right end of it for a change". I knew I had to knock the balls in and I could not rely on Mark to make mistakes.