The Australian finished with a 1-under 70 on Thursday to be four behind joint leaders Steve Stricker and Harrison Frazar at Firestone Country Club.
It threatened to unravel midway through his front nine when the Melburnian made a double-bogey at the par-three 15th. He then dropped a shot on the par-five 16th to slip further down the field.
But a birdie on the 17th, along with others on the second, sixth and ninth - his closing hole - ensured he is right in the mix come Friday, despite one dropped shot on the seventh.
McKenzie is in a tie for ninth with David Toms and Ken Duke, one behind Ernie Els and Justin Leonard (68).
Joint leader Stricker, who won two majors in May and has four tournament victories overall this season, is attempting to run away with the Charles Schwab Cup title. His round Thursday featured an eagle, four birdies and a single bogey.
Stewart Cink is alone in third after a 4-under 66 while South Korean major champion Y.E. Yang is tied for fourth with Germany's Alex Cejka (both 67), a two-time senior major winner.
For now, they're all looking up at Stricker and Frazar, a 51-year-old vet whose last professional victory came in 2011.
Stricker went out on the back nine and birdied Nos. 10 and 13. The eagle came at the par-5, 526-yard second hole, where his hybrid approach rolled to just a few feet of the pin.
More important to Stricker than the holes he scored on were the holes he scrambled to save par.
"It was a combination of everything, right, and this is what this course makes you do," said Stricker, who won this event in 2021.
"You have to scramble going around here, take advantage of the good shots that you have. Tough to get in the fairway at times, and when you don't, you're scrambling to just to make a par, try to get it on the green.
"The rough isn't horrible so you can play out of it, but it doesn't lend itself to being able to attack a pin from the rough."
Frazar also started on the back nine, but his big move came at the turn when he birdied Nos.1, 2 and 3.
"Sometimes you're not as far off as you think you are," Frazar said, "but like I said, attitude was getting in the way more than anything. Just trying to stay level."
Defending champion Jerry Kelly opened with a 1-over 71, as did Germany's Bernhard Langer, who won the US Senior Open earlier this month to become the winningest player in Tour history (46 titles).
Australian Stuart Appleby (70) is tied 12th while compatriot Richard Green (71) is joint 20th.
