Nadal edged all three sets to earn a 6-3, 6-4, 7-6(4) triumph, with his opponent playing some wonderful tennis. Nadal, the top seed and world No. 1, seemed to relish this rigorous examination of his game so early in the tournament.
Elsewhere, there was plenty of drama in the women's bracket, as second seed Caroline Wozniacki produced a thrilling comeback to win her match. Additionally, Elina Svitolina and Jelena Ostapenko—seeded fourth and seventh, respectively—also needed three sets to progress.
It was a fascinating day's play down under. Here are the details on where to catch the action and a recap of Wednesday's highlights.
TV Info: Eurosport 1 (UK) and ESPN2 (U.S.)
Live Stream: Eurosport Player (UK), Tennis Channel Everywhere (U.S.), WatchESPN (U.S.)
Wednesday Replay: Eurosport 1 from 1:30 p.m. (GMT), Tennis Channel from 12 p.m. (ET)
A straight sets win for Nadal at this stage of any competition is often routine, but Mayer made the Spaniard work hard throughout.
In the first two sets, a solitary break of serve was enough for the 16-time Grand Slam champion, although Mayer always posed a threat with some big serving and strong groundstrokes.
The determination of the man from Argentina was epitomised late in the third set, when he broke as Nadal served for the match. However, the Spaniard was able to recover and eventually wrapped it up with a tiebreak.
As we can see courtesy of Eurosport UK, Nadal was extremely respectful of his opponent:
"Leonardo is a player with big potential, he hits the ball so strong," said Nadal after the win, per BBC Sport. "He is a very dangerous opponent. This tournament is my favourite of the year, so I want to stay here as long as possible."
Those in search of drama on Wednesday found it in the women's matches, though, and the showdown between Wozniacki and Jana Fett will surely be a contender for one of the matches of the year.
After losing the opening set, the second seed appeared to have recovered, as she levelled the contest up with ease. However, she stumbled out of the blocks in the decider and was staring at an early exit at 5-1 down.
But from nowhere the Dane was able to pull out a remarkable run of games. She saved two match points and went on to win six games in a row, putting her into Round 3 in the most extraordinary of circumstances.
She posted the following on her Twitter account:
Journalist Nick McCarvel hailed Wozniacki's effort as one of the great comebacks and relayed her post-match emotions:
There was also a scare for French Open champion Ostapenko, as she was involved in a rollercoaster of a clash with Ying-Ying Duan.
Ostapenko appeared on course for a professional win before her opponent rallied with some brilliant play in the second set. In the end, the seventh seed was able to regroup and win through in three sets, although she'll be expecting to improve in Round 3.
Tennis journalist Reem Abulleil paid tribute to her play on the crucial points in this match:
Elsewhere, Svitolina took a while to get going against Katerina Siniakova. She was well below par in the first set, although losing it appeared to jolt the Ukrainian into life, as she dropped just three more games to turn things around.
Other notable wins on Wednesday came from Marin Cilic, as his serve was too hot to handle for Joao Sousa. Home hope Nick Kyrgios is also into Round 3, as he won three tight sets to get the better of Viktor Troicki.