Played in hot and humid conditions on Pat Rafter Arena, the Spanish great took 1hr 23 min to see off Kubler, who battled hard but didn't have the weapons to trouble the 22-time Grand Slam champion.
Nadal, 37, has not played on tour since suffering an injury at the 2023 Australian Open a year ago, resulting in two surgeries on his hip.
He said leading into the tournament he had no expectations for the Australian summer.
But the form he showed against former US Open champion Dominic Thiem in the first round and now Kubler suggests he could be a real threat at the first Grand Slam of the year at Melbourne Park.
He raced to a 5-0 lead in the first set before Kubler got on the board, then broke the Australian's opening game of the second to stamp his authority on the match.
"I started the match playing very well, with very good determination," Nadal said. "I tried to be aggressive from the baseline and I think it worked very well.
"I think it was a very positive match for me. Two victories after a long time being outside the professional tour is something that makes me feel good."
The only real blemish for the Spaniard was a warning for a time violation for taking too long to return to court after a bathroom break at the end of the first set.
He later explained the humidity was so high that he had to do a complete change of clothes and was four seconds longer than he should have been.
Nadal will next play Australian Jordan Thompson in the quarter-finals and remains on course for a blockbuster semi-final against second-seeded Bulgarian Grigor Dimitrov, who demolished Germany's Daniel Altmaier 6-1, 6-2.
Dimitrov served beautifully and pressured Altmaier with some devastating groundstrokes on his way to a comprehensive victory in just 67 minutes.
Dimitrov next meets Australian wildcard Rinky Hijikata, who bounced back from losing the first set to see off Czech qualifier Tomas Machac 5-7, 6-2, 7-6 (7/4).
