In the climactic tiebreaker, Nadal fought off Pouille’s triple match point at 6-3, but the Frenchman won the final two points, the last coming on a blistering forehand winner.
“He’s young. He’s a player that has all the shots. He’s a potential top 10,” Nadal said of Pouille.
songa advanced to a clash against either world number one Novak Djokovic or unseeded Briton Kyle Edmund.
Pouille will next face compatriot Monfils, who has won 18 of his last 20 matches, winning the biggest ATP World Tour title of his career in Washington during that stretch.
“He’s in very good form. He has won so many matches for the last two months,” Pouille said about Monfils.
“But I’m playing well. I have good feelings on the court, so we’ll see.”
Meanwhile, Angelique Kerber won a battle of Grand Slam champions when the second seed powered her way into the quarter-finals on Sunday with a 6-3, 7-5 win over Petra Kvitova.
By reaching the last eight Kerber has put herself in position to end Serena Williams’s long reign as world number one.
Williams, bidding for a record seventh US Open title, will now need to reach the final to have a chance of retaining top spot.
The fourth-round match had a definite Grand Slam pedigree to it with Kerber, the Australian Open champion, going against twice Wimbledon champion Kvitova but failed to deliver any major excitement.
Kerber was in command from the start, winning all the big points on way to taking the opening set.
Kvitova, the Rio Olympic bronze medallist, offered more resistance in the second before meekly surrendering with a double fault on match point to gift Kerber a place in the quarter-finals.
Kerber’s victory set up an intriguing last eight clash with Italy’s Roberta Vinci, last year’s surprise runner-up advancing with a 7-6(5), 6-2 win over Ukraine’s Lesia Tsurenko.