The duo went out together second from last on the famous Old Course after sitting on 10-under from the previous day's action, three shots behind Australia's Cameron Smith.

McIlroy, the 2014 winner, posted his second 66 of the week with five birdies as well as a stunning eagle on the 10th hole where he chipped in from a greenside bunker.

The 33-year-old, the winner of four majors during his career, was only let down by a bogey on a tricky 17th hole.

But McIlroy will start the fourth and final round in pole position to claim the record first prize of $2.5 million (£2.1 million/€2.5 million).

"I'm really pleased," McIlroy told Sky Sports. 

"I missed some chances early on and had to stay patient, but I made my first birdie on the par five and then round got going from there.

"[To win the Open] would mean everything because of what I've been through in the last few years, trying to get that fifth major.

"I need to go out and keep the same mindset I had today.

"Now I need to rest, recover, focus on myself and try to shoot another good one tomorrow."

World ranked number nine Hovland has never recorded a top 10 finish at a major but is contesting for glory in Scotland.

The 24-year-old pulled off six birdies, including four in a row from the third hole, and no dropped shots.

Smith and the United States' Cameron Young went out in the final pairing of the day but Smith bogeyed the first and could not counteract it as he finished on a one-over-par round of 73.

That left him at 12 under for the Championship, level with Young, who has 71.

Kim Si-woo of South Korea and world number one American Scottie Scheffler, the Masters champion, will both go into tomorrow's play at 11 under, while Scheffler's compatriot Dustin Johnson sits on 10 under par.

Tommy Fleetwood shot 66 to place at nine under alongside his fellow Englishman Matt Fitzpatrick, the US Open champion, and Australia's Adam Scott.