McEvoy was briefly two shots clear when he birdied the 14th as well, and although he also birdied the 17th after a bogey on the 16th, the gap was back down to one shot.
England's Tommy Fleetwood, who won his maiden European Tour title in the Johnnie Walker Championship at Gleneagles last month, had birdied the fourth and fifth at Carnoustie, while David Horsey had picked up shots on the fifth, sixth and eighth on the same course.
Wilson, who finished runner-up nine times on The European Tour between 2006 and 2009, had also moved to nine under after hitting his approach to the first at St Andrews to three feet and converting the birdie putt.
Carnoustie usually plays by far the hardest of the three courses, but with scoring conditions excellent Fleetwood birdied the sixth, seventh and eighth to make it five in a row.
That took the 22 year old into the lead on 12 under par, one shot ahead of Denmark's Søren Kjeldsen, who had covered the front nine at St Andrews in 31.
Former champion Martin Kaymer had also moved into contention, the 2010 winner five under for his first 11 holes at Kingsbarns to improve to eight under.