The 25-year-old McIlroy, of Northern Ireland, is fresh off a victory at the European PGA Championship last week, but is seeking his first win on the US PGA Tour since the 2012 BMW Championship.
"I obviously played really well from tee to green. I holed a lot of putts as well, two really good up and downs at the last two holes," said McIlroy.
Masters winner Bubba Watson, Paul Casey and Chris Kirk each posted six-under 66s to share second place, while Keegan Bradley, Michael Thompson and JB Holmes were tied for fifth at five-under 67 at the Muirfield Village Golf Club.
World number one Adam Scott of Australia, who also won last week at the Colonial in Texas, Jordan Spieth and Aaron Baddeley were among a group of 10 players to share 11th place on 69.
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Scott and McIlroy are playing in the same group for the first two rounds of the tournament hosted by Jack Nicklaus. They are joined by Australian Jason Day, who fired an even-par 72.
McIlroy's round included two eagles on the back nine. The world number six also had seven birdies and one double bogey, on the par-four 14th hole.
McIlroy's win last week at Wentworth was his sixth European Tour title but first on European soil.