England's Daniel Gavins, Sweden's Alex Noren and New Zealander Ryan Fox are Mansell's closest challengers.
But on this form they will do well to catch the Englishman at a tournament staged at three Scottish venues, including the Old Course at St Andrews and Kingsbarns.
Mansell was already two shots in front following a fine 68 in atrocious conditions on the nearby Old Course on Friday and so it was no surprise when his good scoring continued on a bright, if breezy, day at the nearby Carnoustie.
He carded six birdies and just one bogey to be 15 under par after three rounds.
Noren spent much of Saturday's play alongside Mansell at the top of the leaderboard but had to sign for a 69 following five birdies and two bogeys.
Gavins and Fox both finished strongly at Kingsbarns to stay in the hunt for victory but Rory McIlroy will need to do something extraordinary on Sunday and hope those above him slump, with the four-time major winner eight shots adrift of Mansell despite a round of 66 at St Andrews.
Robert MacIntyre, bidding to be the first Scottish winner of this event since Colin Montgomerie in 2005, is on the same seven-under mark as McIlroy.
Mansell, chasing a first DP World (European) Tour victory following three top-five finishes this year, said: "I played really, really good. We had one bogey on nine. I hit a good shot in and, again, was just really in control of my golf ball. I've putted good."
He added: "I've been in contention a lot this year and had chances on Sundays. Every time, they say in golf, that you don't lose, you learn. That's what I feel like I've done really well this year.
"Tomorrow there's a lot of golf. It's links golf, anything can happen. It's St Andrews. People can shoot 60. I'm just really focused on myself right now. I'm going to try and shoot a good score and see where it puts me. And just not worry about anyone else."
