US Open champion Gauff prevailed 6-4, 6-2 in her first match of the season, while second-seed Elina Svitolina was also made to struggle before outlasting Caroline Wozniacki 6-4, 6-3 in a battle of the comeback mums.
World number three Gauff raced to a 4-0 lead over Liu, ranked 92 places lower, before the fluidity slipped from her game.
She double-faulted twice to drop her serve and the gap narrowed to 5-4 when Liu broke again.
But the 19-year-old recovered her composure to take the first set when a loose Liu forehand sailed out.
Gauff broke twice more from 3-2 in the second to move into the second-round meeting with 16-year-old Czech Brenda Fruhvirtova.
Gauff declared herself satisfied with her performance as she began her build-up to the Australian Open, beginning on January 14th, despite four double faults and a first serve at only 65 per cent.
"I definitely needed to be tested and I feel like I played well today for my first match in a while," declared Gauff, who is defending the Auckland title she won 12 months ago.
"There's obviously things I can do to improve but I'm happy with the win," she said.
Svitolina and Wozniacki, who both returned to the circuit last year after maternity leave, battled for one hour and 45 minutes before Svitolina triumphed.
Former world number three Svitolina won the opening two games before Wozniacki fought back to lead 4-3.
But another break enabled the Ukrainian to take the first set 6-4.
Svitolina built a 4-1 lead in the second but Wozniacki refused to yield and won the next two games before the Ukrainian stretched away again.
"It was really special for me to get such a great win today against Caroline," said Svitolina, who took a year off to start a family while Wozniacki was away for nearly three years.
"She's a great player and I'm really glad she came back," added Svitolina, who will face either former US Open champion Emma Raducanu of Britain or Spain's Elena-Gabriela Ruse in the second round.
Petra Martic, the seventh seed from Croatia, recovered from a slow start in which she dropped her opening serve and the first set to beat last year's beaten finalist in Auckland, Rebeka Masarova of Spain, 3-6, 6-3, 6-3.
