Carl Desjardins (66), Ken Duke (67), Rob McMillan (68) and overnight co-leader Doug McGuigan (71) are tied for fourth at 7-under-par 137.
Kuehne mixed two birdies and two bogeys on his front side for an even-par 36 but flew out of the gates on the second nine.
He birdied four of his first five holes on the second nine and added a birdie at the par-5 16th to polish off his round of 67.
'Starting out, I didn't strike it well, but my chipping was on all day and I was able to get up and down when I missed greens,' said Kuehne, who won the Texas Challenge in March. 'I know a lot of people come out here to see me hit driver, but they watch me play and realize there is a lot more to my game. No matter how long I hit it, the bottom line is to get the ball in the hole. I take a lot of pride in my entire game.'
Kuehne currently sits second on the Order of Merit list behind another former U.S. Amateur champion, Jeff Quinney. Kuehne played the B.C. Open on the PGA Tour and struggled to an opening-round 76 before firing a second-round 63.
'Those PGA events were a measuring stick, and a lot of the guys were very supportive of me,' said Kuehne, who tied for 19th at the B.C. Open. 'It boosts you confidence playing with them. But right now, my focus is to the win the Order of Merit here. Never mind finishing in the top two. Anyone in my position that tells you they are playing for second is lying.'
Barber, the reigning Order of Merit champion, managed a 2-under-par 70 to reach minus 8.
'I am trying to focus on what I need to do - to get a win this week,' said Barber. 'I was grinding out there, and I am a lot happier with the 70 today than the 66 Thursday. I had to really work for this one, and I am looking forward to a shootout this weekend.'
McKenzie collected seven birdies and two bogeys for his 5-under 67.
Perry Parker, the third co-leader after Thursday's first round, shot an even-par 72 Friday and is part of a group in eighth place at 6-under-par.
The 36-hole cut fell at 1-under-par 143 with 66 players making it to the weekend.
Full-field scores from TELUS Quebec Open