Nadal needed two hours and 38 minutes to continue his bid for his second Australian Open title following his 2009 success, reports Efe.
"For my team and my family, this tournament is their favourite of the year so I want to stay as long as possible," Nadal said after the match.
The 31-year-old Spaniard dominated the encounter, sealing the first two sets thanks to one serve break apiece, while saving all the break points he faced.
However, Nadal saw his serve broken for the only time while serving for the match in the third set's 10th game.
With both holding their next serve, Nadal, the 2017 finalist, got the better of world No. 52 Mayer in the tie break to keep his Australian Open campaign rolling.
In the upcoming round, Nadal is due to play Bosnia's Damir Dzumhur, the world No. 30 who defeated Australia's John Millman 7-5, 3-6, 6-4, 6-1.
The 16-time Grand Slam champion hopes for a better result against Dzumhur as he was forced to withdraw from their lone career match in Miami 2016.
Sixth-seed Marin Cilic also reached the third round, defeating Portugal's Joao Sousa 6-1, 7-5, 6-2.
For a place in the round of 16, the Croatian is set to face the United States' Ryan Harrison, who eliminated Uruguay's Pablo Cuevas 6-4, 7-6 (7-5), 6-4.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
