Johnson, in his fifth visit to Auckland, came to the net regularly but struggled for accuracy and will need to improve to progress further than his semifinal appearance here last year, when he lost to Jack Sock.
The 28-year-old faces a difficult next match in fifth seed Roberto Bautista Agut, the Spaniard fresh off dispatching Kiwi Michael Venus 6-2 6-1 on opening night.
Bautista Agut has won all four previous encounters with Johnson, the last of which was three years ago. Two of those matches went three sets, and their clash at Wimbledon lasted four.
"I've played him a few times and he's got the best of me every time," Johnson said. "I'm going to go out there and try do something different; do what we've been working on and hopefully change the outcome.
"A lot has changed since then so it's a good measure of how both of our games are and where we are to start the year. Hopefully I can build on today and keep getting better."
Elsewhere Korea's Hyeon Chung lost, then regained, his rhythm to battle past lucky loser Tennys Sandgren 6-3 7-5 6-3, and could challenge John Isner if he can return and move the big American around.
Pablo Cuevas, the world No 33, was relatively untroubled against Taro Daniel (world No 98), easing to a 6-3 6-2 win in 76 minutes.
Lukas Lacko made the most of his call up to progress after getting past Stefanos Tsitsipas 6-3 6-7 (5) 6-3 and will meet Robin Haase, who come back to beat qualifier Casper Ruud in three sets.
Jiri Vesely did likewise against Radu Albot with another tough three set (3-6 6-1 7-6 (7) win.
German Peter Gojowczyk survived dropping the first set to American qualifier Tim Smyczek before emerging 3-6 6-4 3-6. His reward is a meeting with defending champion Jack Sock.
