Mackenzie, who led after round one, completed 54 holes at 19-under-par 197 to join second-round leader Bob Estes atop the leaderboard. Estes posted a 4-under 68 in round three to end at minus-19.
Estes will be going for his fifth PGA TOUR crown, but his first since the 2002 Kemper Insurance Open. Mackenzie on the other hand will be searching for his first tour title on Sunday.
John Cook, the 2001 winner here, stands alone in third place at minus-15 after a third-round 69. Daniel Chopra is one stroke further back at 14-under-par 202 thanks to an 8-under 64 in Saturday.
Estes and Mackenzie were paired together in the third round and will be again in Sunday's final round. Both players got on the board with birdies on the par-5 fourth.
Mackenzie came right back with a birdie on the fifth to move into a share of the lead with Estes at 16 under at Montreux Golf and Country Club.
The 30-year-old Mackenzie made it three straight as he birdied the sixth to grab the outright lead by one.
Estes parred three in a row, but matched Mackenzie's birdie on eight to remain one down. They each birdied the par-5 ninth as Mackenzie led by one around the turn.
The 40-year-old Estes grabbed a share of the lead at minus-19 with a birdie on the par-5 11th. He parred his next five as neither player made a move on the back nine.
Mackenzie parred the final nine holes to remain at 19 under.
'I stalled towards the end, I had two real good looks and I had some putts I really didn't understand how to read,' Mackenzie admitted. 'I want to go out and play well Sunday. Regardless I'm going to walk out of here feeling solid and ready for my next tournament.'
He is in the top-15 heading into the final round for the first time in his brief tour career. Mackenzie's best career finish came last year, his rookie year on the PGA TOUR, at the Michelin Championship at Las Vegas, where he shared eighth place.
Estes gave a stroke back to par on the 17th, but atoned for that error at the last where his 17-foot birdie putt gave him a share of the third-round lead.
'Well, I am pretty much where I want to be,' Estes said. 'I was hoping to play a little better than I did today and have a two- or three-shot lead, but I made a few mental mistakes as a lot of people saw on 17. I knew what the play was and didn't do it.'
He leads after three rounds for the ninth time in his TOUR career. Estes won each of the last two times he owned a share of the 54-hole lead. Those wins were at the '02 Kemper and the 2001 FedEx St. Jude Classic.
'You know Will is playing well right now, but neither of us played perfect golf,' admitted Estes. 'Hopefully my experience gives me a little bit of an advantage on Sunday.'
Jeff Brehaut fired a 7-under 65 Saturday to jump to 13-under-par 203. He shares fifth place with Jason Day (67) and 2002 WGC-Accenture Match Play champion Kevin Sutherland (66). Alex Cejka and Shigeki Maruyama are tied for eighth at minus-12.
Yusaku Miyazato, who recorded two holes-in-one on Friday, managed a 2-under 70 in round three. He was joined in 10th place by four others.