Querrey – seeded ninth for the ATP 250 event – needed an hour and 32 minutes as he scraped past compatriot Johnson 7-6 (7-3) 7-5 in the first-round clash in Georgia.
The 2009 runner-up to fellow American Robby Ginepri - a wildcard at this year's tournament - fired down 20 aces and won 88 per cent of his first-serve points.
"This is the time of year where I need to put my foot down and put some results on the table and try to make a jump back into the 20s," the 26-year-old world number 61 said.
"I'm playing through the summer, all six [hard court] tournaments. In the past, this is where I've done well and I'm hoping to do well again."
Next up for Querrey is a second-round meeting with Israeli Dudi Sela.
Sela – still searching for his maiden tour title – thrashed American Donald Young 6-3 6-0.
The 29-year-old, who was beaten by eventual finalist Ivo Karlovic in the last-16 in Bogota last week, wrapped up victory after just an hour on court.