After winning the first set when Rus sent a forehand long, she had to fight back from a break down in the second.
This Williams' first grand slam since taking maternity leave after the birth of Olympia Alexis, her first child with husband Alexis Ohanian.
But Serena has a problem, a unusual distaste for an unglamorous part of her job: drug-testing.
The American admitted, however, that her desire to get back to the top of the game had not been entirely expected. Monday's contest on Court 1 against Arantxa Rus of the Netherlands will be Williams' first since pulling out of the French Open with a hurt chest muscle before a fourth-round showdown with Maria Sharapova.
In other words, Williams was in the mood to gab Sunday at a pre-tournament news conference postponed a day so she could accompany her recently married royal friend, the former Meghan Markle, to watch Prince Harry play polo.
The 23-time Grand Slam champion has now won her last 15 singles matches at Wimbledon after clinching the title in 2015 and 2016.
The 23-time Grand Slam champion wore a head-to-toe white ensemble by Nike - the same brand that created her Wakanda-inspired catsuit to mark her triumphant return to the sport after almost 14 months gone for the birth of daughter Alexis Olympia Ohanian.
Croatia through to quarterfinals after penalty shootout win over Denmark
Real Madrid midfielder Mateo Kovacic, however, has warned his team-mates they will need to keep a close eye on Eriksen on Sunday. Sunday's match got off to an incredible start, and if you were five minutes late, you missed almost everything.
Sloane Stephens fared less well as the French Open finalist became an early casualty, while Victoria Azarenka came away with a sore knee after a nasty slip in her win against Ekaterina Alexandrova. Just due to the numbers, it looks like I'm being pushed out.
The 36-year-old will next take on the victor of Tereza Smitkova's clash with Viktoriya Tomova in the second round. I expected to win this match. I tried to go out there and be aggressive, I was struggling with my serve, it was windy, so I am happy to get through.
The Deadspin article recounted a controversy in which Williams missed a recent drug test. Williams said Sunday that the tester showed up 12 hours earlier than the time they had agreed upon, and she wasn't able to get to the meeting in time.
Harriet Dart's first appearance at Wimbledon - a three-set defeat to Karolina Pliskova - landed her with a windfall of £39,000. "But I am a little bit shocked at how much I nearly want that pressure". "Until I read that article I didn't realize it was such a discrepancy with me as well as against the other players that they listed, at least the American players - both male and female". I know she beat my sister last week in Eastbourne, so I was ready for a tough battle.
Last year's semifinalist Magdalena Rybarikova also exited, losing 7-5, 6-3 to Sorana Cirstea of Romania.
"I'll have to think about it next time".
In the women's event, there were wins for Czech seventh seed Karolína Pliskova who defeated Britain's Harriet Dart 7-6 (7/2), 2-6, 6-1 and 10th seeded American Madison Keys, a 6-4, 6-2 victor over Ajla Tomljanovic of Australia.