World number one Djokovic, the 2011 champion, beat Germany’s Florian Mayer 6-3, 7-5, 6-4, in the Serb’s first grass-court outing of the season and his first match since his shattering five-set semi-final loss to Nadal at the French Open.
“It was a big pleasure to play in front of a packed Centre Court against a tricky rival like Mayer. He’s got a great variety of shots and his game is well-suited to grass,” said Djokovic, who next faces either Bobby Reynolds or Steve Johnson.
Defending champion Williams, chasing a sixth Wimbledon title and 17th major, racked-up her 32nd successive win, cruising to a 6-1, 6-3 win over Luxembourg’s Mandy Minella.
Her 57-minute romp on Centre Court briefly deflected attention away from the storm surrounding her controversial comments on a US high school rape case and the fall-out from her criticism of Maria Sharapova’s love life.
The 31-year-old took out her frustrations on the hapless Minella, the world number 92 who has never defeated a top-30 player let alone one of Williams’s calibre whose French Open title three weeks ago took her majors haul to 16.
Victory was also her 75th in her last 78 matches, a run that stretches back to her shock first round departure at Roland Garros in 2012, the worst Grand Slam exit of her career.
Tuesday’s 32nd successive win took her to within just three of the record set by older sister Venus in 2000.
“I never think about the run, I just treat every match like a new one,” said Williams.
“It was special coming out as defending champion. I played great and I have some great memories.”
Williams did not concede a single point on her serve in the first set and finished the match with 25 winners to Minella’s five.
She goes on to face French qualifier Caroline Garcia, who she beat in the second round in Paris, for a place in the last 32.
Russia’s Maria Kirilenko, who made the quarter-finals last year, slumped to a first round exit at the hands of Britain’s world number 38, Laura Robson, who claimed a 6-3, 6-4 win.
“That was a big one for me just because of all the nerves and playing in front of your home crowd at Wimbledon,” said Robson, a former junior champion.
Kimiko Date-Krumm, just three months shy of her 43rd birthday and the oldest woman in the main draw, made the second round with a 6-0, 6-2 win over Carina Witthoeft, an 18-year-old German qualifier, who was just four when the Japanese star made her Wimbledon debut in 1989.
Date-Krumm, who next faces Romania’s Alexandra Cadantu, said she carefully manages her training schedule to avoid burn-out and drinks a lot of Chinese tea.
“I’m taking care of my body, because of course the most difficult thing is recovery. I need more training. But if I do too much I feel tired,” said Date-Krumm, a semi-finalist in 1996.
“I like Chinese tea. Sometimes Japanese tea. I drink a lot. I have a tea pot I always I carry. It’s here with me now.”
Li Na, the Chinese sixth seed, enjoyed a comprehensive 6-1, 6-1 defeat of Dutchwoman Michaella Krajicek.
The 31-year-old former French Open champion next faces Romania’s Simona Halep.
“It was a pretty good start to Wimbledon. Because the last two years I didn’t do well on the grass court,” said Li, twice a quarter-finalist.
“I have to get used to playing on the grass. I was feeling pretty happy.”
Argentinian eighth seed Juan Martin del Potro, who missed the French Open through illness, saw off Spain’s Albert Ramos 6-2, 7-5, 6-1.
Australia’s Bernard Tomic put out American 21st seed Sam Querrey, 7-6 (8/6), 7-6 (7/3), 3-6, 2-6, 6-3 despite complaining of dizziness midway through the match and being forced to call for a doctor.
Tomic, a quarter-finalist in 2011, was playing without his controversial father in the crowd.
John Tomic, who is facing a criminal charge in Spain for assaulting his son’s hitting partner, has been banned from the club by Wimbledon authorities.