Westwood trailed McIlroy by nine strokes after carding a six-under-par 65 at Congressional Country Club on Saturday and questioned the tournament front-runner's ability to cope with the last-day pressure.
"You don't know how Rory is going to do," world number two Westwood told reporters after storming up the leaderboard with a sizzling birdie-birdie-birdie-eagle run on the back nine.
"You don't know how he's going to deal with the big lead. He had a big lead in a Major and didn't deal with it well before."
Northern Irishman McIlroy held a four-stroke lead going into the final round of this year's Masters but wilted under the pressure with an ugly closing 80 to tumble out of contention.
"There's pressure on him with regards to that," Englishman Westwood said. "So we'll see. All I can do is control my game and try and shoot as low a score as possible for me. They don't give trophies away on Fridays and Saturdays."
Like McIlroy, Westwood is bidding for his first Major title and he was elated with his performance in the last two rounds at Congressional after opening with a 75.
"I'm happy to be in the tournament," said the 38-year-old who has twice been a runner-up in the Majors along with three third-place finishes. "I thought I was going home after my round on Thursday, I played dreadful.
"Today I drove the ball great. I put myself in position to be able to attack the flags. If you drive the ball well around this golf course, it's score-able."
Asked how he would approach Sunday's final round with McIlroy seemingly in cruise control, Westwood replied: "I've set a target on Friday night. That's all you can do when you're chasing a big lead.
"I can't control how Rory is going to play, nor can he control my game. So I'll do that. My mission was to get myself somewhere into the tournament. I said maybe if I can get to 10 under at the weekend."