Amid the course hardening up and scoring becoming more difficult for the field, it was Mulroy who fired his best round of the week, a level par 70, which helped the player climb 17 places on the day into a share of 16th.
German Martin Kaymer still leads by five shots despite a third round 72, on eight under, heading into the final round.
Mulroy lies on three over for the tournament, and if he is able to match his third round return, a top 15 automatic invite to next year’s event beckons.
One South African player who will be eyeing a top 15 finish is Retief Goosen, who shot a third round 71 to finish at five over in a tie for 30th with one round remaining.
The former world-number three has had his ranking drop to 214th in the world, but one last good round would secure his entry to the 2015 US Open.
Goosen, a two-time US Open champion with his last victory coming in 2004, is playing in his final edition of his 10 year exemption into the event.
“I hope for another, if I can get a nice low round in tomorrow and get myself back in the top,” said Goosen after his round.
“So I’m hoping for a nice round tomorrow and to enjoy it.
“I’ve had a good run in the US Open and if I make it into next year… great.”
Goosen’s round of 71 on Saturday was one of the better scores on the day, but ‘The Goose’ felt his play was not his best.
“I actually didn’t play that well today, tee to green,” said Goosen.
“I missed a lot of fairways, but I got a bit lucky in that wispy stuff and I made a few great up-and-downs. I made a lot of very good up-and-downs.”
Ernie Els was a shot further back on six over after a third round 72, while compatriot Louis Oosthuizen battled his way to a 78 for 12 over overall to drop to 61st spot on the leaderboard.
– Sapa
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