Resuming 5-3 clear from the morning session, Masters champion Allen won the first frame of the second session for a 6-3 lead only for the world number 56 Stevens to produce breaks of 110 and 144, his highest competitive contribution since 2012.
A clearly buzzing Stevens was first among the balls in the 12th frame, but broke down on 33 as Allen returned to the table to make a lovely 102 to maintain his two-frame advantage at 7-5 clear.
Allen beats Robertson in phenomenally high-standard final
Former Masters and UK champion Stevens responded with 115 after the mid-session interval, but was again at a loss on 44 in the 14th frame with Allen capitalising with an 85 that carried him one frame from the winning post.
Both men had chances in the 15th frame, but Allen was largely the dominant force, aided by a run of 44, to reach the final of this event for a third time despite Stevens clawing out one of three snookers he required on the final red.
In a match that contained five centuries including 11 breaks over 50, it was a pity that there has to be a loser with Allen remaining supremely calm to benefit from the rare errors that came off his opponent's cue.
World number 12 Allen - who lost the 2014 final 10-7 to Ricky Walden and by the same scoreline against Mark Selby a year ago - will face Neil Robertson or Jack Lisowski in the best-of-19 frame final on Sunday with a top prize of £175,000 on the line.
FIRST SESSION REPORT
Mark Allen won the final four frames of the first session of his International Championship semi-final with Matthews Stevens to lead 5-3 before they play to a finish on Friday afternoon.
The Masters champion won the first frame of the day with a 75 only to watch Stevens - playing close to the level that won him the Masters in 2000 and the UK title three years later - reel off three straight frames with breaks of 59, 70 and 86.
The Welshman was again first among the balls in the fifth frame, but could not piece together a winning run as Allen stemmed the tide by winning a scrappy frame to trail 3-2.
It proved a major turning point as the Northern Irishman embarked on breaks of 70 and 120 to establish a 4-3 advantage having looked likely to trail 4-1.
Stevens had the chance to level the session at 4-4, but suffered agony as a mid-range pinked stayed up, enabling Allen to pot a tricky pink with the rest plus a black for a 5-3 advantage heading into the closing session.
The second session is LIVE on Eurosport 1 at 11:30am (GMT) on Friday with the first man to nine frames reaching Sunday's final.
The second semi-final is on Saturday (6am and 11:30am) when 2012 finalist Neil Robertson meets Jack Lisowski, a repeat of their Riga Masters final in July that Robertson won 5-2.
Watch Roberton's lovely double against Lisowski
Watch Roberton finish off classy century break to stretch lead over Lisowski