Darren Clarke and Graeme McDowell posted impressive third rounds to move up the leaderboard into joint 12th place on five under par at the Open.
Starting on the 10th hole, Clarke fired a five-under 67, the joint best round of the day, including six birdies in seven holes from the 17th to the fifth.
McDowell carded six birdies and two bogeys for a 68 at Hoylake, including five birdies on his inward nine.
Rory McIlroy shot a 68 to end the day on 16 under, six ahead of the field.
Rickie Fowler is his nearest challenger on 10 under, with just Sunday's final 18 holes to come.
Shane Lowry lies tied for 23rd on three under after a third round of two-under 70.
Play began earlier than originally anticipated on Saturday because of a poor weather forecast, including the possibility of thunder and lightning, which never materialised.
As a result, the players took to the course in groups of three and started at both the first and 10th holes.
Clarke's round was marred by a solitary bogey on the third, which came midway through the 2011 champion's hot streak of birdies.
The Dungannon player had registered successive level par rounds of 72 on the opening two days at Royal Liverpool.
McDowell has recovered from a disappointing first-round 74 to record under-par rounds of 69 and 68.
"The weather was pretty nasty when I started off and the front nine didn't go my way," said McDowell after his third round.
"I took on a few flags when I didn't need to, but the back nine was kinder to me and I made a few birdies.
"I'm too far back to think of winning though - the leaders are just out of touching distance," added the former US Open champion.