Earlier, French qualifier Adrian Mannarino ousted fifth-seeded South African Kevin Anderson 6-3, 6-3, while eighth-seeded German Philipp Kohlschreiber struggled past Swiss qualifier Stephan Bohli 6-4, 4-6, 6-4.
Both Harrison and Querrey entered the tournament on wild cards and the 19-year-old Harrison proved more consistent than Querrey, whose ranking has dropped from 17 to 94 after a series of injuries.
"I played well from start to finish and it was a great match for me," Harrison said. "Getting the first match of the season out of the way with a win is always exciting.
"I didn't expect a quick match against a player like Sam, but I served well and played well and I'm very happy."
Mannarino continued his strong form in Auckland to beat Anderson in 64 minutes. He was a quarterfinalist at the tournament last year and won three qualifying matches easily to reach the main draw.
The 6-foot-8 Anderson started emphatically with three aces in his first service game, but Mannarino's return of serve became more and more potent, blunting the South African's main weapon.
Mannarino broke in the third and ninth games of the first set and in the sixth game of the second while never facing a break point on his own serve.
"I really played well," Mannarino said. "Last year I played so good here and this year seems to be the same."
Kohlschreiber also continued his outstanding record in Auckland by beating the plucky Bohli. The German improved his record in Auckland to 17 wins from 22 games after winning the title in 2008, reaching the semifinals in 2010 and the quarters on four occasions.
He struggled at first, putting only 43 percent of first serves in play in the first set and dropping to barely 30 percent in the second. But the 28-year-old stepped up his effort in the deciding set, breaking Bohli in the seventh game.
"It was just a tough challenge today, Kohlschreiber said. "Arriving on Sunday from Doha, it was tougher to play this game.
"I wasn't moving well. I was a bit stiff in the back at times and he gave me a tough challenge but I'm happy to be through."
Olivier Rochus of Belgium struggled to beat sixth-seeded Thomaz Bellucci of Brazil 7-6 (6), 5-7, 7-6 (5) in a match that lasted more than three hours, while second-seeded Nicolas Almagro of Spain advanced comfortably, serving 11 aces to beat Santiago Giraldo of Colombia 6-4, 6-2.