Norwegian Durasovic, ranked 354, 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).
That would certainly have been a relief after the drama of his seven missed match points against Dominik Koepfer in Paris last week.
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 20-year-old Italian Sinner, who narrowly missed out on a place at the ATP Finals.
It will be a first competitive meeting between the pair, and Murray said: “He’s one of the best players in the world. Yes he’s obviously young but he’s ranked in the top 10 in the world.
“Certainly on this surface, he’s maybe the best of the young ones. Indoor hard courts I think is a good surface for him, he’s won a number of tournaments on these sort of courts so it’s a good match for me to get at this stage of the season.”
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.
Carril helped Johanna Konta develop into a top-10 player and is a well-known figure within British tennis, most recently working with Katie Swan.
He also had a trial with Emma Raducanu but she has opted for German Torben Beltz and, after helping Swan win a title in Estonia on Sunday, Carril headed straight to Stockholm.
Murray said: “He has a very good reputation, certainly in British tennis, and he’s done a very good job with a number of players in the UK.
“I’ve always had a couple of coaches working with me. I think having a bit of space and distance is important. It’s a very, very intense relationship between player and coach on the tour.
“These last few years have been tough for me and my team. There’s been a lot of time spent together but also a lot of difficult moments because of the nature of the injuries and then some of the tennis hasn’t been great at times.”
On his first impressions of Carril, Murray said: “He’s very calm and considered. He’s a good communicator as well, which is certainly not one of my strengths, so it’s something that I look for in a coach.”
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies