The 14-time grand slam winner, who has dropped to ninth in the world rankings after struggling with injuries in recent seasons, needed two hours and 56 minutes to see off the Frenchman 6-3 6-3 4-6 6-4 at the Rod Laver Arena.
Nadal, a winner in Melbourne in 2009, has played better in his distinguished career, but the former world No. 1 celebrated wildly nevertheless as he won.
Looking for his first title at one of tennis' four majors since the French Open in 2014, Nadal described the victory as "very special."
"I started well and had a few chances in the third, and then it was difficult in the fourth," the 30-year-old said during an on-court interview.
"Then at the end of the match, Gael made a few mistakes and I played a good backhand on the break point and it meant the world that game."
Nadal's joy was understandable given it was his first victory over a top-10 player at a grand slam since his triumph at Roland Garros almost three years ago. It also ended a four-match losing streak against top-10 opponents.
Nadal's progress also keeps alive the mouthwatering prospect of a final against Roger Federer, who advanced to the quarterfinals after a five-set battle with Kei Nishikori.
The two old rivals have both struggled to hit the heights in recent seasons. Federer is playing his first competitive tournament since Wimbledon six months ago, following a knee injury, and dropped out of the world's top 10 for the first time in 734 weeks last November.
But with world No. 1 Andy Murray and defending champion Novak Djokovic suffering shock defeats in the opening week, both Nadal and Federer will sense an opportunity to make a statement in Melbourne.
Nadal, however, must first get past third seed Milos Raonic, last year's Wimbledon finalist, to stand a chance of renewing his battle with Federer.
"I need to be very focused with my serve and play aggressive," added the former champion, who was beaten by Raonic in Brisbane earlier this month.
"If I am not playing aggressive then I am dead because he plays aggressive."
Serena sets up Konta tie
Elsewhere, second seed Serena Williams overcame Czech Barbora Strycova 7-5 6-4 to set up a quarterfinal tie with Britain's Johanna Konta.
"I love pressure. I feel like I deal well with pressure. I love the game, I love being out here," said the six-time champion.
"Honestly, I have nothing to lose. Everything is a bonus for me right now so it's kind of a little relaxing."