Perhaps mindful of the fading light, Williams sped to a 5-0 lead after 15 minutes before recovering from a mid-set slump to claim it 6-3.
The second seed faced a long wait for action on Court One but her focus remained firmly intact as she began the match at 7.26pm with an ace before continuing to serve viciously during a first game in which her opponent failed to land a shot in the court.
Williams lost the next two points but recovered to break and did so again without losing a point in the fourth game, after another powerful service game.
The five-times winner produced another perfect service game but her 34-year-old opponent put up a better fight in the sixth game, eventually getting off the mark with a pass shot greeted warmly by the crowd.
The Paraguayan continued to improve and earned break point after a long rally before a backhand cross-court effort pulled the score back to 5-2.
De los Rios held serve again and her increasing confidence was evident when she lobbed Williams brilliantly, but the favourite soon clinched the set with an ace.
Three Britons crashed out as the opening day in south London served up all-too familiar heartache for home fans.
Laura Robson, Elena Baltacha and Melanie South all fell at the first hurdle.
French Open champion Francesca Schiavone could not maintain the form which brought her Roland Garros glory as she made a swift exit.
The Italian, who turns 30 tomorrow, was a shock winner of the Paris title earlier this month when she defeated another surprise finalist, Australian Sam Stosur.
That maiden grand slam victory of her career nudged her up the rankings, elevated her profile, and resulted in her being made fifth seed for Wimbledon.
But she was on the end of a major first-round upset as Russian Vera Dushevina battled back from dropping the first set to win 6-7 (0/7) 7-5 6-1 on Court Two.
Elena Baltacha admitted she had cracked under pressure after slumping a first-round defeat to an opponent making her Wimbledon and grass-court debut.
The British number one marked her ninth appearance at the All England Club with a dire 2-6 7-5 6-3 loss to 19-year-old Croatian Petra Martic.
Serving for the match at 5-4 up in the second set, Baltacha’s temperament failed her at the crucial moment as she endured her fifth first-round exit from the tournament.
The 26-year-old, playing a solid though under-whelming opponent positioned 24 places lower in the world rankings at 76, never recovered once the panic had set in.
“I’ll be honest – I was actually quite tight at 5-4 up.
“I was nervous. Up until that point I was in control,” said Baltacha.
“I tried to stay as relaxed as I could but I got slightly tight. I’m human – I’m not a machine. Sometimes things like that happen.
“It was a big occasion. I was serving for the match at Wimbledon and playing here is always very special.
“When you get to Wimbledon you will feel nervous because as a Brit you’re expected to do things. The thing is how you manage those.”