The American had missed a tricky eagle putt to set a European Tour record 59 on Friday, and went about continuing his fine form with five birdies in the first nine holes.
Two further birdies were cancelled out by a pair of bogeys but his eagle on the 18th propelled him into the outright lead on 20-under.
Joost Luiten, David Howell, Ernie Els, Richard McEvoy, Martin Kaymer and Shane Lowry form a formidable chasing pack on 18-under.
"I wasn't quite sure what I was going to do with my second shot but it worked out well and when I saw it go in, it was pretty sweet and a nice way to sign off," said Uihlein.
"And to play the Old Course for a first time was awesome and it's one of the best, if not the best golf course in the world."