McIlroy started the third Major of the year with a 66 to lead by one shot, and Scott, who finished the day just two strokes off the pace, is hopeful he can prevent the Northern Irishman from extending the gap at Royal Liverpool.
"It's important, you've got to keep pace with a guy like Rory," the Australian told reporters. "He has the potential to really put his foot down. I've seen him shoot lots of low rounds, and there's nothing stopping him from doing that tomorrow, either.
"I don't want him running away. We've seen what happens, he wins Majors by eight shots. Martin Kaymer did it just a few weeks ago in the US Open, and it makes for a tough weekend when you're that far behind having to force it."
Scott was one of seven players to reach four-under-par, with just McIlroy and Matteo Manassero ahead of the group after 18 holes.