It took four hours and a fifth-set tiebreak to upset the world No.5, which earns the 22-year-old a quarterfinal berth, alongside compatriots Gael Monfils and Jo-Wilfried Tsonga. He will meet Monfils in the next round.
Pouille refused to be drawn on the long-term impact of his historic win over the 14-time slam winner. "Maybe it will change my career, but I will see," he said.
"It will give me a lot of confidence for the next round, for the rest of the season."
The world No. 25 faltered briefly during the fifth set before recovering to win the tie-break 6-1 2-6 6-4 3-6 7-6 (8-6) and secure an historic victory over a player who hasn't missed a quarterfinal date in 12 years.
Pouille also made the quarterfinals at Wimbledon earlier this year, but to beat a player of Nadal's stature will rank as perhaps his greatest on-court achievement.
Sevastova inks in QF date
Elsewhere at Flushing Meadows, unseeded Latvian Anastasija Sevastova, currently ranked 48th in the world, created her own upset Sunday when she knocked out the British 13th seed Johanna Konta.
Her 6-4 7-5 win earns the 27-year-old a last eight tie with Dane Caroline Wozniacki, who also sailed through her match, beating eighth seed Madison Keys 6-3 6-4.
Konta did not appear to be at her best in the Arthur Ashe Stadium. She collapsed on court during her second-round victory at Flushing Meadows.
"I'm sure there are some remnants of it but it's not the reason I lost today," Konta told reporters. My opponent played an overall more solid match than I did," she said.
Wozniacki made the final at Flushing Meadows in 2009 and 2014 but a series of fitness problems, including an ankle injury earlier this year, have seen her drop to 74th in the world rankings.
It is the second time in the tournament that Sevastova has upset the form book. She knocked out third seed Garbine Muguruza in the second round.
On the US Open website, Sevastova said she has been fighting hard for victory after recovering from a string of injuries since her layoff in 2013.
"But now, I'm back," she said.
Seventh seed Roberta Vinci (Italy) is also through to the quarters after beating Ukrainian Lesia Tsurenko 7-6 6-2 and will now face either second seed Angelique Kerber (Germany) or Czech player Petra Kvitova in the next round.
In the men's competition, the ninth seed Jo-Wilfried Tsonga (France) needed five sets to overcome American Jack Sock 6-3 6-3 7-6 6-2. He will now meet either top seed Novak Djokovic or Briton Kyle Edmund in the quarter final.