The 34-year-old had led by two at the halfway stage but was caught at the summit early in his third round on Saturday before three birdies in four holes from the fourth took him four shots clear.
Tarren then saw his advantage wiped out altogether as bogeys on the eighth, 11th and 12th dropped him back to 13 under par, where he had started the day.
But he was never overtaken at the top and safely parred his way home to keep his nose in front of a high-quality chasing pack just one shot back.
Englishmen Dan Brown and Brandon Robinson-Thompson were in a tie for second on 12 under alongside Spain's Pablo Larrazabal and Italian Francesco Laporta.
Tarren was pleased with the way he hung in there as he signed for a level-par 72, saying: "I'm a bit frustrated really. I got off to such a good start, felt so comfortable.
"I just missed a few putts in that mid-section of the round, three-putted the eighth, a short one at the ninth, a good chance at the 10th and didn't capitalise.
"I've felt comfortable all week and I felt comfortable out there today. The start showed it - through seven holes I was cruising.
"Just a couple of missed putts here and there, but that's golf. Final group tomorrow again and I have the lead so there's lots of positives to take from it."
Australian Jason Scrivener was way back in the pack in joint-32nd position after his 73 left him at four under, while David Micheluzzi was tied for 55th on one under for the week after his 73.
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