The Dublin native completed 54 holes at 4-under-par 212 at Adare Manor Hotel & Golf Resort.
Bradley Dredge carded the low round of the day with a 3-under 69. He vaulted from a share of 17th into a tie for second at 1-under-par 215 and was joined there by Simon Wakefield, who managed a 1-over 73 in the third round.
Richard Green (72) and Louis Oosthuizen (73) are tied for fourth at even-par 216.
Conditions were much improved from the first two days, but the scoring did not get much better. Just four players broke par in the third round and five more shot even-par 72 on Saturday.
Harrington, who will try to become the first Irishman to win this event since John O'Leary in 1982, rolled in a long birdie putt on the first to move to 4 under.
After dropping a shot at the sixth, Harrington also bogeyed the par-5 seventh to slide out of the lead at minus-2.
The Irishman steadied himself with four straight pars while regaining the lead as Wakefield dropped a pair of strokes early on the back nine.
Harrington missed a couple of makable birdie tries on the back nine before getting to minus-4 with a 5-foot birdie putt at 17. He could have extended his lead to four strokes, but missed an 8-footer for birdie at the last.
Wakefield, in the final pairing with Harrington, birdied the second but gave that stroke right back when he bogeyed the third. He drained a 14-foot birdie putt at the seventh to take the lead at 3 under.
Around the turn, though, things started to fall apart. Wakefield three-putted for bogey on the 10th and then could not save par after missing the green at the 11th.
Those bogeys dropped him to minus-1 and more trouble was on the horizon. He rolled his third shot to 5 feet at the 14th, but missed the par-saving putt to slip to even-par for the tournament.
Wakefield did get one stroke back with a birdie on 16, but he parred the final two holes to end three back.
Dredge made his run late in the day. He was even-par for his round after nine holes with a pair of bogeys and birdies, then ran off three birdies in a four-hole stretch from the 15th to finish at 1 under.
Damien McGrane carded one of the four sub-par rounds with a 2-under 70. That helped him jump from a share of 25th into a tie for sixth at plus-1 alongside Andres Romero.
Joakim Backstrom, Alastair Forsyth, Raphael Jacquelin and Francesco Molinari are tied for eighth at 2-over-par 218.