Disappointed with his work on the greens during an opening round of 68, Johnson grabbed a fresh putter and, after just 20 minutes of practice, put it to brilliant use on the back nine at Sheshan Golf Club.
Four behind at the start of the day, the rangy American rolled in seven birdies after the turn, including four in succession on his last four holes.
"Obviously I played very well today, I actually got a putter about 20 minutes before I teed off," the 2016 U.S. Open winner said after his bogey-free round.
"I wasn't really pleased with the one I played with yesterday.
"I was coming from the range when I grabbed (the new one). I had a few putts on the practice green ... and then I came out and holed a few putts."
After opening with two straight birdies, U.S. Open champion Koepka laboured through a frustrating run of 13 straight pars before breaking the birdie drought on the par-four 16th.
Another birdie on 17 gave him the chance to reel in Johnson on the par-five 18th but he had to be content with a closing par after burning the edge of the cup with a putt from six feet.
Henrik Stenson remains in contention after shooting a 69. The Swede sits six strokes behind Johnson and level with Matt Kuchar (70) in a group of four on seven-under.
Former world number one Jason Day, however, endured a torrid 74 littered with five bogeys and is 12 off the pace on one-under with Phil Mickelson (72).
Hideki Matsuyama's title defence appears all but over after the Japanese carded a second straight 74.
(Reporting by Ian Ransom in Melbourne; Editing by Peter Rutherford)
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