Resuming from overnight at 3-3 in the first set, and with Murray holding a break point, the 29-year-old Serbian managed to stave off the initial threat before conceding his serve two points later.
It took Murray just seven minutes to wrap up the opening set ??? for the loss of just two points ??? but faced a sterner challenge in the second.
Troicki???s slow start may have been due to the injury he suffered on the wet Queen???s Club surface on Saturday when he fell heavily and hurt his left shoulder.
But he responded well in the second set and registered the first break of serve in game five.
However, from 2-4 down, Murray broke back at the first opportunity when his opponent netted a fairly routine forehand volley at 30-40.
The world No 25 did well to take the second set into a tie-break, after trailing 5-6 and 0-30.
But despite claiming a 2-0 lead in the tie-break, Troicki was unable to maintain the momentum allowing Murray to take charge, with the Scot winning seven of the final nine points.
Murray now meets world No 17 Kevin Anderson in Sunday???s final, when he could make it a record-equalling fourth title ??? which would take him level with John McEnroe, Boris Becker, Lleyton Hewitt and Andy Roddick.