The Northern Irishman is currently joint-top of the leaderboard heading into the final round of the 150th Open Championship at St Andrews.
Encouraged by an excellent eagle from a bunker on the 10th hole, McIlroy produced a round of 66 to significantly boost his hopes of ending his eight-year wait for a major.
A bogey on the ever-troublesome Road Hole 17th prevented McIlroy, who is bidding to become the first European winner on the Old Course since Nick Faldo in 1990, from taking an outright lead.
The 33-year-old shares the lead with Ryder Cup teammate Viktor Hovland, who also carded a round of 66 to continue his hopes of a first major title.
McIlroy claimed the famous Claret Jug back in 2014, and won his fourth major in the US PGA just a month later. However, he hasn't been able to win one of the four major crowns since.
The world number two revealed his career will not be complete unless he wins the Open Championship at St Andrews.
"I don't know if a golfer's career isn't complete if you don't, but I think it's the Holy Grail of our sport," McIlroy said in his pre-tournament press conference on Tuesday.
Asked about the significance of winning on Sunday, McIlroy told Sky Sports: "It would mean everything because of what I have been through the last few years, trying to get the fifth one.
"I have a lot of belief in myself, I know I can do it again. I just need to go out in my own little world and shoot a good score that I know I can do around here."
Cameron Smith started the third round in pole position, but slipped down the standings with a double bogey on the 13th.
The Australian now heads into the final round four shots adrift of the leading pair. He is joined on 12 under by American Cameron Young.