Norwegian Durasovic, ranked 354 in the world, put up a good fight in the second set having been overwhelmed in the opener but Murray survived another tight tie-break to win 6-1, 7-6 (7).
He saw two more go begging having led 6-4 in the tie-break but this time Murray completed the job on his third chance and will now take on Sinner, who narrowly missed out on a place at the ATP Finals.
Murray is trialling a new coach this week in Esteban Carril with a view to the Spaniard joining Jamie Delgado in the Scot’s team for next season.
He said: “I still believe I have some good tennis left in me, I want to try and have some more big tournaments.”
Murray faces Italian 20-year-old Jannik Sinner on Wednesday for a place in the quarter-finals, and expects a tough match with the tournament’s top seed.
The Scot noted: “[Sinner]’s had a fantastic year, he was very unlucky not to make the [ATP Finals] in Turin. I think he’s won four or five tournaments this year and he loves playing indoors on hard courts so it should be a big test for me – it should be a good one.”
Additional reporting by PA Media.