17th major, cruised 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 the calibre of Williams, 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 but Minella, playing in only her eighth Grand Slam compared to the American's 52nd, at least had the consolation of breaking her opponent's serve for a 2-0 lead in the second set.
But she couldn't capitalise on that slim opening and Williams roared back, finishing the match with 25 winners to Minella's five.
Williams goes on to face French qualifier Caroline Garcia, who she beat in the second round in Paris, for a place in the last 32.
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," she said.
"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, raced into the second round with 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."
Li's compatriot Zheng Jie missed the chance of setting up a rematch with Williams when she lost 6-3, 6-4 to 100-ranked Garcia.
Zheng, the world number 47 who made the semi-finals in 2008, gave Williams a scare last year at Wimbledon, with the American winning 9-7 in the final set of a roller-coaster encounter.
Later Tuesday, men's top seed Novak Djokovic, the 2011 champion, starts his campaign against Germany's Florian Mayer who he beat in the quarter-finals last year.
In early action, Argentina 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.