The world number one will now meet John Higgins in Saturday afternoon's semi-final in a heavyweight collision.
Allen began sharply, compiling breaks of 69 and 76 to reach the mid-session interval locked at 2-2.
At that point, the Northern Irishman, ranked 10th in the world and traditionally a difficult opponent for Trump, appeared the more assured player, controlling the table and dictating tempo.
The turning point arrived early in frame five. Allen missed a mid-range red to the right corner that would likely have given him the lead, and Trump pounced.
Until then, his highest contribution had been a modest 35, but under pressure, he cleared the table with a composed half-century to steal the frame by a single point.
A break of 70 carried Trump further clear, before a fluent 68 in the following frame underlined the gulf that had opened up. What had been a finely balanced contest became a demonstration of Trump's ability to punish even the slightest lapse.
Trump and Higgins have contested World Championship finals in 2011 and 2019, but this will mark their first encounter at the Masters.
Trump arrives with a psychological edge, having won their last seven meetings, and will be keen to extend that run on one of the sport's most unforgiving stages.
For Trump, this is an eighth Masters semi-final and another opportunity to add to a growing legacy at the event. Champion in 2019 and again in 2023, has not lifted a trophy since the 2024 UK Championship, a drought that has lingered despite his continued dominance of the rankings.
"I didn't have my A-game today and I had to dig deep at 2-2 to make that big important clearance and the game kind of turned after that," Trump said afterwards.
"I never play my best against him but I didn't need it at the end today, which is lucky for me."