Nadal said his lower-back stiffness was continuing to improve after his 6-3, 6-4, 6-2 against the flamboyant Italian, which set up a quarter-final against Greece’s Stefanos Tsitsipas.
Fognini had registered a five-set win over Nadal at the 2015 US Open, but the Spaniard cantered to victory after recovering from 2-4 down in the second set.
Nadal is now into his 43rd Grand Slam quarter-final, staying on course for a title match with eight-time winner Novak Djokovic who battled through an abdominal injury to reach the last eight on Sunday.
“I’m happy to be in the quarter-finals today -- that means a lot to me, it’s positive stuff,” said Nadal, who is level with Roger Federer on 20 Grand Slam men’s singles titles.
Next up for Nadal is world number six Tsitsipas, who went through on a walkover after Italy’s Matteo Berrettini pulled out with an abdominal strain.
The Melbourne tournament remained fan-free for a third day on Monday during a five-day lockdown in Victoria state to curb a coronavirus outbreak.
As the action continued in front of empty stands, top-ranked Barty beat big-hitting American Shelby Rogers in impressive fashion to reach the last eight.
Barty won 6-3, 6-4 to go into the quarter-finals without dropping a set as she bids to become the first Australian champion since Chris O’Neil in 1978.
“I love playing at home and sharing this with my friends and family,” said Barty, who hit 21 winners.
The former French Open champion next plays Karolina Muchova, who came through two tight sets to beat Belgium’s Elise Mertens 7-6 (7/5), 7-5.
Elsewhere, fourth seed Daniil Medvedev and seventh seed Andrey Rublev both won to ensure an all-Russian quarter-final.
Medvedev, the 2019 US Open runner-up, blew away American world number 192 Mackenzie McDonald 6-4, 6-2, 6-3 to extend his winning streak to 18 matches.
Rublev, who is also unbeaten this year, went through when Norway’s Casper Ruud retired after losing the first two sets.