The Northern Irishman carded a third-round 68 for a 16-under-par total, with American Rickie Fowler his nearest contender on 10 under.
McIlroy, 25, won from seven back at the PGA Championship at Wentworth in May.
"I know leads can go quickly," he said. "That's why you can't let yourself think about winning."
McIlroy was tied with Fowler on 12 under after 13 holes but eagles at the 16th and 18th helped him to the biggest 54-hole advantage at the Open since Tiger Woods led by six at St Andrews in 2000.
But McIlroy - whose father Gerry and three friends placed a bet £400 at 500-1 10 years ago that he would win the Open by the time he was 25 - is well aware what the pressure of leading a major tournament can do to a player, having blown a four-shot lead on the final day of the Masters in 2011 and eventually carded an 80.
Open 2014: Rickie Fowler challenges - top five shots"I've been on the right side of it and I've been on the wrong side of it," said the 25-year-old, who has led from the opening day.
"You've just got to stay completely in the moment and that's what I'm going to do for all 18 holes tomorrow."
Fowler will tee off with his old rival in the final pairing on Sunday, having carded a third-round 68, and has not given up hope of overhauling him.
"If I can get off to a good start and put pressure on, there is a lot of golf to be played," said the 25-year-old American, whose rivalry with McIlroy dates back to when they faced each other in the 2007 Walker Cup.
"Being alongside Rory is an advantage. We are going to have a good time, so much can happen so quickly."
Fowler drew level at one stage on Saturday but stumbled down the back nine before also carding a 68.
Sergio Garcia is one shot behind Fowler and level with American Dustin Johnson but the Spaniard also held out hope of landing his first major title.
McIlroy's third round in 60 seconds"I am a little bit disappointed with the way I played the last two holes," said Garcia, whose third-round 69 would have been better but for a bogey at the 17th and a scratchy par at the par-five 18th.
"It is never easy being in the position of leader. Rory is a great player but you never know, anything can happen.
"But you can't just attack everything because you are not going to hit good shots. You have to attack where you feel comfortable attacking."
Meanwhile, world number one Adam Scott has not ruled out the possibility of somebody setting a record score for a major championship on the final day.
The Australian carded a third-round 69 to finish 10 shots behind McIlroy but believes a score of 62 is achievable, if Sunday delivers good weather.
"If we have similar conditions to today, there are low scores out there," said former Masters champion Scott.
"If you can get it going for 18 holes, there's a chance for that major scoring record to be broken.
"I think out of the group of the guys up there, there's probably a low score in one of them."
Garcia, like Fowler, is seeking his first major title, having achieved seven top-10 finishes in the Open
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