The second-seeded Nadal hadn't played a match since claiming his 11th French Open title last month, but showed little sign of rust as he cruised to victory.
Federer, the only semi-finalist from a year ago left in either of the singles draws, will face France's Adrian Mannarino on Monday.
"I felt much more confident in my game, I served better and I felt so pumped", said Pella, who reached the third round of a major for the first time.
Ekaterina Makarova of Russian Federation also reached the fourth round, following up her victory over second-seeded Caroline Wozniacki with a 4-6, 6-4, 6-1 win over former semifinalist Lucie Safarova of the Czech Republic.
South Africa's Kevin Anderson, seeded eight, swept past Germany's Philipp Kohlschreiber 6-3, 7-5, 7-5 on the back of 22 aces and 42 winners.
She is the fourth former women's champion to get knocked out, joining Maria Sharapova, Petra Kvitova and last year's victor Garbine Muguruza.
That would be Serena Williams, the 23-time Grand Slam-titleholder, who fought off unseeded Kristina Mladenovic of France 7-5, 7-6 (2).
The top seed, who is yet to drop a set at this year's championships, did not relinquish a single break point during the 97-minute domination.
Venus had rallied from a set down in her first two matches.
This Saturday will see Rafael Nadal in the third round of Wimbledon for the eighth time in his career.
He is on a great run at Wimbledon since the start of 2017, winning 29 consecutive sets here which is his second longest streak after 2005-2006 when he rattled off 34.
"I'm happy to be through".
However, she lost her way after that and went a set and 4-0 down before recomposing herself and taking it to a third.
Monfils is another fourth round debutant after he knocked out last year's semi-finalist Sam Querrey 5-7 6-4 6-4 6-2.
They traded breaks mid-set and Mladenovic did well to hold from 15-40 in the 10th game - just seven points from going out of the tournament.
Keys added: "It's definitely been a challenge that I have had to deal with where all of a sudden I'm the one that's supposed to win and people are playing with nothing to lose and playing their best tennis".