The 34-year-old Wilson is now 15 under for the tournament after 54 holes and in prime position to achieve a maiden European Tour victory.
Wilson, who played on the losing European Ryder Cup in 2008 but is now ranked 792 in the world, has been a perennial runner-up since turning professional in 2003.
He has finished second on nine occasions including the 2009 Dunhill Championship when he ended the tournament three shots behind England's Simon Dyson.
But he will begin Sunday's final round with a healthy advantage on McIlroy, Tommy Fleetwood, Alexander Levy and overnight leader Raphael Jacquelin.
"I'm pretty happy with that," said Wilson. "I played good today, left a lot out there, as well, which is a bit frustrating but obviously I'm pleased with how I played, especially coming down the stretch, hit a lot of good shots.
"I expect Rory to shoot lights out every time he tees it up. The other names that are on the board don't really affect me.
"I'm just doing my thing, trying to shoot as good a score as I can, get it in play, one shot at a time, all the boring stuff, but it's true. I managed to do that really well.
"There's 18 holes, long holes, and it's going to be a long day tomorrow, but it would mean a lot. I'll be nervous. It's a big day for me. Last year I got off to a great start and kind of fizzled out in a similar kind of position really."
The event is being played on the Old Course at St Andrews, Kingsbarns and Carnoustie with the field rotating courses.
Englishman Fleetwood covered his opening nine holes in five under par and finished with a ten under par 62 in the round of the day on the Old Course to lie joint second with Northern Irishman McIlroy and the French duo Levy and Jacquelin.
McIlroy, fresh from his triumph at the Ryder Cup, had a blistering front nine that saw him reel off eight birdies in ten holes, including five in a row to catapult up the leaderboard.
"I got off to a really fast start and was trying to keep it going, and I sort of did through the turn," said McIlroy, who is also playing the pro-am event with his dad Gerry.
"The last four holes weren't really what I wanted. But any time you shoot a score like that around St Andrews, you have to be happy."
"Dad and I are going to play St Andrews on his birthday tomorrow (55th) which will be a huge treat for both of us," added McIlroy.
Fleetwood, who recently finished second at the Wales Open, had a run of six birdies in a row around the turn and ten in total as he chases a second European victory.
Lanky Englishman Chris Wood carded a bogey free round 66 on the Kingsbarns layout and is tied for sixth along with American Ryan Palmer, who signed for his third straight round in the 60s and Scotland's Richie Ramsey.
201 - Oliver Wilson 64 72 65
204 - Tommy Fleetwood 69 73 62, Rory McIlroy 73 67 64, Alexander Levy (FRA) 68 68 68, Raphael Jacquelin (FRA) 65 70 69
205 - Chris Wood 70 69 66, Ryan Palmer (USA) 69 68 68, Richie Ramsay 69 68 68
206 - Robert-Jan Derksen (NED) 73 70 63, George Coetzee (RSA) 71 67 68, Louis Oosthuizen (RSA) 70 74 62
207 - Chris Doak 70 67 70, Stephen Gallacher 68 70 69, Shane Lowry 66 70 71, Padraig Harrington 66 70 71, Michael Hoey 72 70 65, Brooks Koepka (USA) 70 73 64, Richard Sterne (RSA) 73 66 68
208 - Alejandro Canizares (ESP) 72 71 65, Marcel Siem (GER) 69 71 68, Robert Karlsson (SWE) 72 68 68, Paul Casey 69 73 66