Nadal and the Frenchman traded blows from the baseline during an engrossing 30-point tiebreaker lasting almost half an hour. The opening set lasted one hour and 21 minutes, Reuters reported.
"The first set was very, very emotional," sixth seed Nadal, who saved four set points during the tiebreaker, said at Rod Laver Arena.
"Anything could have happened there. I was a little bit lucky at the end.
"Everybody knows how mentally (tough) this game is. It was a tough one and after that crazy first set, I think it was so important the break at the beginning of the second set."
Mannarino had lost both his previous meetings against Nadal and came into the contest after a demanding third-round victory over Russian Aslan Karatsev in a match that lasted four hours and 39 minutes.
After the energy-sapping first set under the blazing afternoon sun at Melbourne Park's main showcourt, the 69th-ranked Frenchman wilted as Nadal went on to seal the win with an ace on his first match point.
Nadal's last defeat by another left-hander in a contested match came in 2017 against Denis Shapovalov, who will be his next opponent after the Canadian saw off German third seed Alexander Zverev in straight sets.
"After that match I said he's going to be a potential multi-Grand Slam winner," Nadal said of the 22-year-old. "And I still think that if he's able to keep improving, he will be a multi-Grand Slam winner.
"He has a lot of amazing things in his game, and his results say that. When he's playing well, it's very difficult to stop him."
The only former champion left in the men's draw, 2009 winner Nadal is tied on 20 majors with injured Roger Federer and nine-times Melbourne Park winner Novak Djokovic, who was deported before the tournament began.
A second title at Melbourne Park would not only break the three-way tie at the top of men's tennis but also make Nadal just the second man after Djokovic to win each of the four Grand Slams twice since the sport became professional in 1968.
But his lead-up to the hardcourt major has been far from ideal. The 35-year-old returned to the Tour after spending four months on the sidelines due to a long-standing foot problem and also contracted COVID-19 last month.
"I am enjoying the fact that I am here and I am enjoying the fact that I am again in a quarter-finals of a Grand Slam, something that's very special for me," he said.