"The greens are really tricky, but I have done a really good job of controlling the distance with my irons and give myself lots of looks at birdies," Johnson told Golf Channel.
A winner two years ago at the high-altitude course outside Mexico City, the American said he enjoyed playing the challenging layout.
"It makes you focus. You've got to think," Johnson added. "You are doing a lot of calculations with the numbers and trying to figure out how far the ball is actually going to go.
"It is pretty narrow, but it is tree lined, so I do like that."
Overnight leader McIlroy, who shot a first-round 63, looked set to break open the tournament with birdies at three of his first four holes but a bogey at the sixth and a double at the ninth left him with a 70.
Kuchar's six-birdie 67 kept him at the top end of the leaderboard, while Tiger Woods and defending champion Phil Mickelson were on the move.
Woods found his putting touch to advance to within six shots of the lead with a 66 and Mickelson rebounded from an opening 79 with the joint best round of the day, a 65.
Playing in Mexico for the first time, Woods was satisfied with his round after posting six birdies and only one bogey.
"I think I got a little more familiar with the golf course," he said.
"I got a better feel for the tee shots, the lines, the approach shots and the greens.
"It helped having that one look yesterday in a competitive environment."
England's Tommy Fleetwood and Spaniard Sergio Garcia were tied for fourth on seven-under.
Fleetwood started his day with back-to-back eagles and matched Mickelson's 65, while Garcia shot a 66.
(Reporting by Gene Cherry in Raleigh, North Carolina, editing by Nick Mulvenney)
