The world number one Spaniard's march towards a 17th Grand Slam crown was never threatened by Argentina's Leonardo Mayer, who took him to a third set tiebreak before being swatted aside 6-3, 6-4, 7-6 (7/4) on Rod Laver Arena.
"Playing this court is always a big motivation for me," said Nadal, who lost last year's final to Roger Federer.
"He was a dangerous opponent and I'm happy to be in the third round.
"For my team and my family, this is our favourite tournament of the year, so I hope to stay around a bit longer," he added.
Nadal, showing no signs of the troublesome knee that bothered him late last season and interrupted his Melbourne lead-up, next plays Bosnian 28th seed Damir Dzumhur.
Surprisingly, he was not the prime time men's night match on centre court, with that honour going to third seed Dimitrov, who survived a huge scare from unheralded qualifier Mackenzie McDonald.
The Bulgarian needed to call on all his experience to down the 186th-ranked American 4-6, 6-2, 6-4, 0-6, 8-6.
"I'm very happy with the win, not because the way I played, but because the way I fought," said Dimitrov. "It all came down to a few points here and there."
In contrast to Nadal's easy progress, world number two Wozniacki also struggled against little-known Croat Jana Fett.
The Dane saved two match points and rallied from 5-1 down in an epic third set to keep her dream of a first Grand Slam title alive.
She looked out for the count, and was struggling afterwards to work out how she survived 3-6, 6-2, 7-5 against a player ranked 119.
"That was crazy, I don't how I got back in the match," said Wozniacki, adding that "experience was crucial".
- 'I'm talented' -
Fourth seed Elina Svitolina also came from a set down to overcome spirited Czech Katerina Siniakova 4-6, 6-2, 6-1.
The Ukrainian is now on a seven-match win streak and after picking up five WTA Tour titles last year, more than any other woman, is a serious Grand Slam contender.
Her next task is tackling 15-year-old sensation Marta Kostyuk, who became the youngest woman to reach the third round since Martina Hingis got to the quarter-finals in 1996.
Also Ukrainian, she beat local wildcard Olivia Rogowska 6-3, 7-5.
Her win streak at Melbourne Park is now 11 straight matches after claiming the Australian Open girls' title in 2017 and coming through qualifying this year.
"I heard a lot of times that I'm talented, and I know that," said the confident teen. "But I know that only talent will not help me to play good. So I'm working pretty hard."
Svitolina said she knew little about the youngster, and was preparing for a no-holds barred fight.
"She has nothing to lose, so that's why I know she goes just for everything. You know, a little bit like a headless chicken," she said.
French Open champion and seventh seed Jelena Ostapenko also progressed, but she too needed three sets to get past China's Duan Yingying.
On a hot Melbourne day, Croatia's sixth seed Marin Cilic advanced, with last year's Wimbledon finalist easily beating Joao Sousa.
US Open semi-finalist and 10th seed Pablo Carreno-Busta also went through after French veteran Gilles Simon retired injured when trailing 6-2, 3-0.
And fighting former finalist Jo-Wilfried Tsonga saw off rising Canadian youngster Denis Shapovalov in a five-set thriller.
But Russia's Anastasia Pavlyuchenkova, a quarter-finalist last year, became the latest seed to slump out in the women's draw, which has been shorn of leading names over the first two rounds.
Venus Williams' conqueror Belinda Bencic also ran out of steam, having no answers against Thai qualifier Luksika Kumkhum, slumping out 6-1, 6-3.
Source: AFP
GMT 08:49 2018 Monday ,22 January
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All rights reserved to Arab Today Media Group 2023 ©
Maintained and developed by Arabs Today Group SAL.
All rights reserved to Arab Today Media Group 2023 ©