The 34-year-old from Northern Ireland, trying to win his first major since 2014, fired a second straight one-under par 69 to stand on one-under 209 through 54 holes at soggy Oak Hill.
That's five adrift of leader Brooks Koepka, the same gap McIlroy had on the lead through 36 holes. But this time, McIlroy sees how he is able to hang tough when his game is sketchy at best.
"My attitude has been well, my ability to just stick in there and show a little bit of grit and determination and not let rounds get away from me too much," he said.
"I made two good putts for bogeys on the sixth and seventh. Doing things like that, not letting the round really get away from you, that's what I've done well this week."
McIlroy, who took a mental health break after missing the cut at the Masters, has fought off illness and lacklustre play to be in the hunt.
"I'd like to be a couple shots closer to the lead, but with how I've felt this week, if you had told me on Thursday night I'd be going into Sunday in the top five and with a realistic chance to win this golf tournament, I would have taken it."
McIlroy battled through a day-long deluge in difficult conditions with a game more scrambling than solid.
"I still don't feel like my game is in great shape. I've held it together well," McIlroy said. "I've holed some good putts. I've scored well.
"The non-physical parts of the game I think are way more important this week than the physical parts of the game, and I think I've done those well, and that's the reason that I'm in a decent position."
With five birdies and four bogeys, McIlroy said making a run for the trophy will require doing away with his mistakes and turn a 69 into a 65.
"I made enough birdies to shoot a score like that. I just needed to keep those mistakes off the card," McIlroy said.
"I need to keep hope. I have to believe that there is a score like that out there because looking at the board, it's probably a score I'm going to have to shoot, something like that, to have a chance to win."
