Welshman Bradley Dredge had a four-shot lead heading into Saturday's play at the Himmerland Golf and Spa Resort in Aalborg, but went two over for his round and is tied with Warren on six under overall ahead of the final round on Sunday.
The field was met with winds of up to 30 miles per hour, yet Scot Warren contended the difficult conditions superbly with eight birdies, including a run of four in five holes between the 13th and 17th.
Warren was particularly impressive with the putter and, had it not been for three bogeys, he would have been the outright leader.
Indeed, Dredge - whose two birdies were negated by four bogeys - dropped a shot at the 15th and only held on to a share of the lead with a three at the par-four 17th.
Dredge then held to par at the last, keeping his nerve despite a delay when someone collapsed and required medical treatment.
Warren, who has not won on the European Tour since 2007, said: "Even driving here you could see the wind was a lot stronger than the first two days. I knew it would be a battle.
"Obviously Bradley was a bit ahead and I was hoping it was going to be a bit tougher. If it was easier he could have pulled away. So overall I'm delighted. To shoot 66, I probably couldn't have hoped for that before."
Northern Ireland's Gareth Maybin shot himself into contention with a round of 68 and is three shots off the pace, as is Simon Wakefield, who signed for a one-over 72.
Stuart Manley, Phillip Archer and Thorbjorn Olesen are four shots adrift.
Elsewhere, Michael Hoey confirmed on Twitter that he had withdrawn from the tournament after mistakenly believing he had missed the cut.
The Northern Irishman wrongly believed he had failed to make the weekend's play and subsequently headed for Amsterdam and, having heard he had made the cut, missed his return flight because his clubs had been lost by the airline he was travelling with.