Rahm, who outscored playing partner and defending champion McIlroy by 13 shots over the first two days, carded a third round of 67 to finish 17 under par, a total matched by American Daniel Im.
The world No.11 took advantage of glorious conditions at Portstewart Golf Club to fire six birdies and a solitary bogey, four of the birdies coming in succession from the 11th.
Since turning professional just over a year ago, Rahm has claimed his first PGA Tour title and racked up a string of impressive performances, including finishing third and second in his first two World Golf Championship events.
And the 22-year-old now has the chance of following in the footsteps of fellow Spaniards Seve Ballesteros, Jose Maria Olazabal and Sergio Garcia in winning the Irish Open.
“It could be a very special day tomorrow,” said Rahm, who described his adventurous birdie on the par-five 14th as a “Seve birdie.”
“This tournament has a good Spanish history and it would be great to join that. I’ve never led going into the final round so I am a little inexperienced in that sense, but I know what I did at Torrey Pines [where he won the Farmers Insurance Open], both good and bad. Hopefully I won’t need two eagles in the last five holes again to win. I have exceeded my expectations. My putting and short game has never been my best ally on links courses, but this week has been the opposite. I’m not used to making this many putts and it feels great.”
Rahm, who is playing just his second regular European Tour event and finished 10th in the HNA Open de France last week, added: “Before I won at Torrey Pines this was not a possibility.
“The only chance to come and play would be to be invited. Winning that tournament meant I was able to come here and pick and choose events. So to achieve a goal that was not even in my mind at the start of the year would be very special.”
Im is ranked 542nd in the world but handled the pressure of the halfway lead in impressive fashion, carding five birdies and one bogey in a third round of 68.
“I think I’m just going to enjoy every moment of it tomorrow,” Im said. “It’s always good to be on top of the leaderboard. I’m just going to go out there and do my own thing and see what happens at the end.
“It’s going to be amazing playing with Jon Rahm. He’s one of the fastest-rising stars in the world. I think it will be fun.”
France’s Benjamin Hebert was a shot off the lead after a 69, with Japan’s Hideto Tanihara on 15 under and France’s Julien Quesne a shot further back after equalling the course record with a superb 64.
Also on fine form was Scotland’s Scott Jamieson whose 66 lifted him into a share of 12th place, on 11 under, six shots off the lead. He is tied with compatriot Richie Ramsay who enjoyed a 67 yesterday. It was a disappointing day for David Drysdale who dropped back following a 73 and is now tied with Stephen Gallacher (72) on eight under. Duncan Stewart, the fifth Scot to make the cut, also shot 72 and is on five under.
Olympic champion Justin Rose was part of a four-strong group on 13 under after a bogey-free 66 which was amazingly compiled despite hitting just one fairway.
“To go bogey-free on a day when you don’t really have your best golf is exactly what I need at this point,” Rose said. “It’s really sharpened up my short game this week after a couple of weeks off. Ahead of the Open Championship at Birkdale I’ve certainly tested myself, my scrambling capabilities, but come through so far strongly this week and it would be nice to start ironing out a few other tweaks and I’ll be feeling pretty good about things.”
There was bad news for Rose’s Ryder Cup team-mate Jamie Donaldson, who was tied 12th after 36 holes but was forced to withdrew before the start of his round with a pulled muscle in his back. Donaldson was 25th in the world when he secured the winning point at Gleneagles in 2014, but has since slipped to 231st after a loss of form and various injuries, including one to his left hand caused by an accident with a chainsaw in 2016.