A third successive 67 on the picturesque Aviemore course cemented the 27-year-old's position at the top of the leaderboard ahead of Sweden's Magnus Carlsson (69) and Norwegian Marius Thorp (67), with another Scot, Chris Doak, just four shots off the pace alongside Mark Tullo of Chile.
In what has been an encouraging event so far for the home contingent, defending champion Jamie McLeary is also still in the hunt for a 27,000 top prize after he shot a second successive 68 to move up 10 places to joint-10th.
One ahead at the start of an overcast day on Speyside, Murray had increased his advantage to three after going out in 31, four-under. He stumbled slightly with back-to-back bogeys at the 11th and 12th but repaired that damage with an eagle three at the 523-yard 17th, where he holed a 35-footer across the green.
"It would be brilliant if I could record my first professional win in Scotland and if I can keep doing what I've been doing so far this week, then hopefully I'll be okay. However, there is nothing I can do if someone goes daft tomorrow and shoots seven-under."
Doak, who booked into the same place he stayed when winning the Northern Open over the same course two years ago, kept his title hopes alive with a 68 and is getting good omens as he chases a 27,000 first prize that would allow him to play on the Challenge Tour for the rest of the season.
The 32-year-old from Greenock was out in 31, four-under, before chipping in for a two at the 10th to move to 10-under for the tournament. However, a double-bogey six at the 11th undid some of his good work and he covered the final seven holes in level-par.
"I'm playing well and am still in contention," he said. "I'm on the same score as I was after 54 holes when I won the Northern Open."
McLeary wasn't making much headway after covering his opening eight holes in one-over but then holed his second shot from 102 yards for an eagle at the 330-yard ninth. After seeing birdie putts horseshoe out at both the 12th and 13th, he holed one from 30 feet to pick up a shot at the 15th before a two-putt birdie at the long 17th gave him a second successive 68 and 54-hole total of 207.
"I keep all my stats and have been consistent all year. I'm 12-under for all my rounds, averaging 70.8 compared to 71.7 the previous year – a massive difference," added McLeary.