World number five Sabalenka, who warmed up for Melbourne Park by winning the Adelaide title, mowed down Tereza Martincova in her opener but struggled for rhythm in the opening exchanges with Rogers, dropping serve early in the first set.
The Belarusian soon hit her stride, however, and powered past the American to close out the match and stay unbeaten in six matches this year.
Sabalenka's lack of major titles has often been ascribed to the inconsistency of her serve but it has looked much improved and she is yet to lose a set in six matches this year.
While Rogers' hopes of an upset came to nothing fellow American Katie Volynets stunned ninth seed Veronika Kudermetova 6-4 2-6 6-2 in just her sixth main draw appearance at a Grand Slam, the world number 113 revelling in the Margaret Court Arena atmosphere.
"I've never played in a stadium this packed and that many people keeping the energy up for me," said Volynets, who became the first U.S. qualifier to reach round three in women's singles at Melbourne Park since Lindsay Davenport in 1993.
Magda Linette later joined fellow Pole and top seed Iga Swiatek in the third round with a 3-6 6-3 6-4 upset of 16th seed Anett Kontaveit, while Croatian Donna Vekic downed 18th seed Liudmila Samsonova 6-3 6-0.
A moment of controversy saw Frenchman Jeremy Chardy lose his cool in his 6-4 6-4 6-1 defeat by Briton Dan Evans. Chardy unloaded on the chair umpire after she did not order a point replayed when a ball fell out of the Frenchman's pocket during a rally.
"In my life, 20 years, I've never had one umpire bad like you," he told umpire Miriam Bley. "Where are you looking? You looking at the birds? The clouds?
"It's the biggest mistake of the Australian Open. There's not one umpire on tour that does this mistake, not one."
Evans will next meet Russian fifth seed Andrey Rublev, who beat Finn Emil Ruusuvuori 6-2 6-4 6-7(2) 6-3.
Rublev suffered a setback in the third set, after a row with the umpire over whether the fifth seed was swearing in Russian.
J.J. Wolf joined them in the next round after he beat Argentine Diego Schwartzman, the 23rd seed, 6-1 6-4 6-4.
The home crowd rose to acknowledge the retiring Sam Stosur, who lost in the first round of the women's doubles with Alize Cornet. The 38-year-old major winner still has the mixed doubles to come, where she will partner Matt Ebden.
After two days of severe weather disruptions, Melbourne Park escaped extreme heat or rain on Thursday with organisers on track to get the second round completed on schedule.
