Warren had been tied for the lead at the halfway stage at Royal Aberdeen with Rose a shot off the pace, and both men continued their consistent form to set up an exciting conclusion on Sunday.
Former US champion Rose carded a five-under 66, while Warren was left to rue a bogey at the last as he gave up the chance of holding the lead outright.
Kristoffer Broberg, who had been tied with Warren after round two, is a shot behind the top pair, while fellow overnight leader Ricardo Gonzalez shot a level-par 71 to fall four back, tied for fifth.
Rory McIlroy's topsy-turvy week continued, the Northern Irishman currently tied for 13th along with three others - seven shots behind Rose and Warren.
The former world number one shot a course-record 64 on Thursday, before a 78 on Friday was followed up by a three-under 68 in the third round.
Rose - who birdied six holes, including five of the back nine - was pleased with his progress ahead of The Open Championship, starting on Thursday.
"I came here on Wednesday and felt absolutely horrendous but the last couple of days I have been finding my feet again and that's part of the reason for playing here," he said.
"Today and my second round at Congressional are two of the best rounds I have played all year. I'm really happy with the way the game has progressed throughout the week.
"It would be great to win tomorrow. I'm on a nice run at the moment and to keep it going would be fantastic. I'm still really enjoying the links golf and I think that's what I came here to do, just keep playing the game and keep trying to work out the shots.
"But obviously there will come a point tomorrow where you have to win a golf tournament. I'm looking forward to it.
"I said at the beginning of the week, just to be in contention this week and sharpening your skills under pressure will be a fantastic opportunity going into the Open next week."