In the men's tournament, Roger Federer's latest victory never looked in doubt as he won 37 of 40 first-serve points and stretched his Wimbledon winning streak to 29 sets, beating Jan-Lennard Struff of Germany 6-3, 7-5, 6-2.
Serena will play world number 120 Rodina if she advances to the fourth round.
Heather Watson and her partner Tatjana Maria also ensured they had a place in the third round of the women's doubles with a routine 6-3 6-1 win over Raquel Atawo and Anna-Lena Gronefeld.
Venus had rallied from a set down in her first two matches.
"It was very tough because he played very well", said 11-time French Open champion Nadal, who is chasing an 18th major. It is timed for release as the anticipation crests with Roger as returning champion, 10 years after their famed 2008 Wimbledon championship - an epic match so close and so reflective of their competitive balance that, in the end, the true victor was the sport itself.
Struggling to stay in the set after half an hour, Williams found her huge serve just in time to hang on for 4-5.
The defeat of the U.S. Open runner-up meant she became the seventh casualty in the top 10 women's seeds before the middle weekend.
The 36-year-old American will face another mother in the fourth round Monday: 120th-ranked qualifier Evgeniya Rodina of Russian Federation, who upset No. 10 seed Madison Keys of the U.S. "You have to win the last point, and I didn't succeed in that today".More news: Brazil, Belgium Target World Cup Quarters After Spain Bow Out
"Serena is my idol", Rodina said.
The defending champion made light work of his first two opponents in SW19 and it was a familiar story today as he clinched a 6-3 7-5 6-2 win.
Keys lost nine games on the trot from 5-2 up in the first set to 0-4 down in the second.
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.
The 38-year-old, seeded ninth, was a set and a break down but battled back to square the match, only to lose 8-6 in the decider.
Donna Vekic reached the fourth round of a Grand Slam for the first time in her career with a 7-6 (7-2) 6-1 victory against Yanina Wickmayer.
"I worked really, really hard (to get back playing) and it's been a long, arduous road but I always expected to come out and do the best I can do".