"I think I played a solid match", said Nadal, who will face John Isner of the United States in the quarter-finals tomorrow.
The world number one, who was beaten by Pouille the last time they met at the 2016 U.S. Open, lost a close first set before saving two match points in a second-set tiebreak which he won to level things up. But still I didn't have the control of the match for nearly all the time. Tomorrow will be a tough one against Isner; he's playing unbelievably well.
The in-form American, the sixth seed, is renowned for his booming service game and Nadal expects to come under a barrage today.
Mayer didn't convert a break point in the first game of the match and a game point in the second and fourth game.
Second seed Alexander Zverev served seven aces as he beat Britain's Kyle Edmund 6-3 7-6 (3) in the day's last match and will meet Italy's Fabio Fognini in the next round.
Also into the quarter-finals are Caroline Garcia, who defeated French compatriot Alize Cornet 6-2, 6-1, and Czech Barbora Strycova, who beat Daria Gavrilova of Australia 6-0, 6-4.
In the women's draw, former world No. 1 and fourth seed Karolina Pliskova became the latest high-profile casualty, going out in the third round to unseeded Sorana Cirstea.
"The doctor suggested I should take a period of rest and get it treated, but I can only rest after the season, that's the plan", said Peng, ranked 25 in the world. The Spaniard is coming off a big win in the US Open and he is full of confidence playing on the hard court like he will be in this game.