Rose and Warren (67) are on 10-under-par overall at the warm-up tournament for the British Open, one shot clear of Kristoffer Broberg of Sweden (68).
Nearly three weeks after winning the Quicken Loans National at Congressional to end a yearlong drought, Rose has kept up his strong form despite struggling with hayfever and, more recently, sinus pains.
His round was the joint lowest of the day and he had the best back nine of the field, a 31 containing five birdies that was some effort considering it was into the wind off the North Sea.
''Probably my second round at Congressional and this round are two of the best I've played all year,'' said Rose, whose last victory before Congressional was the 2013 U.S. Open at Merion. ''I felt like I got it close to the hole many times out there, which on a links course is hard to do.
''I'm on a nice little run right now. To keep it going would be fantastic.''
Warren, who held a three-shot lead midway through the third round, is looking to avenge a final-round collapse at his home Scottish Open in 2012. He also had near misses from good positions at the Spanish Open and the BMW PGA Championship in 2013.
Warren will have the support of the majority of the crowd in what will be an England vs. Scotland contest on Sunday.
''For a Scottish guy, it doesn't get much better than this. It's our fifth major,'' said Warren, whose two victories on the European Tour came in 2006 and `07. ''Playing with Justin Rose will just add to the occasion as well.''
Conditions were much more benign compared to Friday, but Rory McIlroy (68) and defending champion Phil Mickelson (70) were unable to mount considerable challenges to the leaders and are seven and eight shots off the lead, respectively.
Both, however, are happy with their links game ahead of the British Open at Hoylake.
''I have shot a 64 and a 68 on this golf course, two really good scores,'' said McIlroy, who followed up his course-record score in the first round with a 78 on Friday. ''It would be nice to shoot another one good tomorrow ... but I feel good with my game and I see enough positives in there to give me confidence going in.''
Tyrrell Hatton of England is alone in fourth on 7 under after a 66.
While Warren has picked up a reputation of cracking under pressure, the No. 6-ranked Rose is increasingly becoming known as a winner over tough courses.
His resume includes victories at Merion, Doral, Valderrama, Muirfield Village and most recently Congressional - and that makes him the favorite going into Sunday.
''This would hold its own among the courses I have won on,'' Rose said. ''They've all been on pretty stout tests. I'll take pride on winning on a links course, that is for sure.''
Rose has been struggling with hayfever since returning from the United States two weeks ago, and he wore sunglasses during his third round despite it being foggy. He said Saturday was the worst he'd felt all week.
''I felt a little bit achy, a little bit of a headache and sinus pain,'' Rose said. ''I need to get on top of it before next week.''