Mansell struggled to a closing 76 and finished tied for seventh as Fox shot 68 to win on 15 under.
Northern Ireland’s Rory McIlroy tied for fourth, a shot behind Englishman Shinkwin and Swede Noren, and one ahead of England’s Daniel Gavins.
Fox had regularly played the event with the late Australian cricket great Shane Warne.
And Fox told BBC Scotland: “I felt that Warney was with me this week. You need a little bit of luck in golf and I felt that he was that today.”
“He absolutely loved this tournament and we had an awful lot of fun here over the years. A lot of people missed him this week including myself but I’m pretty proud to get the job done and remember him like that.”
After the field had played Carnoustie, Kingsbarns, and the Old Course over the first three days, all returned to the ‘Home of Golf’ for the final round.
Fox picked up four birdies on his front nine and three more comings home, with three bogeys meaning he was four under for the day.
Noren’s third successive three-under 69 and Shinkwin’s 67 put them in contention but Fox made par on the 18th to seal the victory.
“I wouldn’t say I came into this week with any good form – with a couple of missed cuts and a withdrawal – but I always felt that this week was going to be a little different,” Fox added.
Forrest’s Tour Card
Grant Forrest and Connor Syme were the highest-placed Scots in a tie for 10th on 10 under while Italian Open champion Robert MacIntyre was two shots further back alongside three-time major winner Padraig Harrington.
Forrest says the top-10 finish will go a long way to helping him secure his tour card with just five regular events left in this campaign.
“It’s been a struggle this season,” he said. “I was struggling off the tee and the ball just wasn’t going where I wanted it to go. It’s frustrating. You come out from your best year ever last year and your expectations are to be doing better every year, which I have done until this year.
“It takes you to some pretty dark places but you just have to dig in and all it takes is just one week and you find something and start playing well again.”