The playing partners entered Moving Day at the Old Course three shots off the lead but produced matching rounds of 66 to get to 16 under and hold a four-shot advantage over Australian Cameron Smith and American Cameron Young.
World Number One Scottie Scheffler and South Korean Si Woo Kim were at 11 under, a shot clear of American Dustin Johnson and two ahead of English pair Matt Fitzpatrick and Tommy Fleetwood and birthday boy Adam Scott.
But all eyes will be on the European Ryder Cup duo on the final day, as Hovland goes in search of a first Major Championship and McIlroy a fifth, and second Claret Jug.
Both McIlroy and Hovland are in the top ten of the DP World Tour Rankings in Partnership with Rolex, with the Northern Irishman finishing in the top ten at the previous three Major Championships and the top three at the Slync.io Dubai Desert Classic.
Hovland was the winner in the United Arab Emirates as he claimed a first Rolex Series victory but he has yet to finish in the top ten at a Major.
McIlroy has a win of his own in 2022 at the RBC Canadian Open on the PGA TOUR and everything is set up for a thrilling duel on Championship Sunday at the Home of Golf.
“It would mean everything because of what I have been through the last few years, trying to get the fifth one," said McIlroy of a potential victory.
“I have a lot of belief in myself, I know I can do it again. I just need to go out in my own little world and shoot a good score that I know I can do around here.
It's unbelievably cool to have a chance to win The Open at St Andrews. It's what dreams are made of and I'm going to try to make a dream come true tomorrow - Rory McIlroy
"The galleries have been massive. The ovations coming on the greens, with the big grandstands.
"I think it's appreciating the moment as well and appreciating the fact that it's unbelievably cool to have a chance to win The Open at St Andrews. It's what dreams are made of and I'm going to try to make a dream come true tomorrow."
Overnight leader Smith three-putted the first to see his advantage trimmed to one shot but Hovland was having no problems with the short stick as he soon moved into a share.
The 24-year-old holed from 38 feet on the third and was even more impressive on the fourth, making a 42-foot right-to-lefter down the bank for a second consecutive birdie.
He made it three in a row with two putts on the fifth and playing partner McIlroy also took advantage of the par five in similar fashion to sit two back.
McIlroy also birdied the next after an approach to six feet but he did not get any closer to the lead as Hovland made his gain from 19 feet.
The gap was cut as McIlroy drove the ninth and got down in two and he then catapulted to the top of the leaderboard on the next with a spectacular holed bunker shot for an eagle that brought an enormous roar from the crowds.
Hovland made a birdie at the same hole as he two-putted from just off the green but McIlroy regained the solo lead with a two-putt gain of his own on the par-five 14th.
Just to be here is very special but to have a chance to win one, I have to pinch myself, but that doesn't mean I'm going to hold back tomorrow - Viktor Hovland
He bogeyed the Road Hole after going over the green as Hovland made an impressive par save but the pair both made two-putt birdies on the last to give themselves a comfortable cushion over the chasing pack.
Victory would make Hovland the first ever male Major Championship winner from Norway and the historical significance was not lost on the two-time DP World Tour winner.
"I don't think there's any other place that would top it," he said.
"It's pretty crazy from where I grew up and so far away from playing the PGA TOUR, DP World Tour, for that matter Major Championships. Just to be here is very special but to have a chance to win one, I have to pinch myself, but that doesn't mean I'm going to hold back tomorrow.
"The support I've been seeing the last couple of years in Norway has been really cool because we've always been kind of a winter nation and done well in the Olympics.
"Hopefully we could have a similar impact to when Henrik (Stenson) won The Open a few years ago and just get more people to play golf and watch it on TV."
Smith carded a 73 to fall back, while playing partner Young made a double-bogey on the 16th in his 71.
Kim carded a 67, Scheffler recorded a 69 and Johnson signed for a 71, with Fleetwood, Fitzpatrick and Scott registering rounds of 66, 69 and 70 respectively.