The 34-year-old six-time champion battled to a 6-2, 6-4 win over Swiss qualifier Amra Sadikovic, ranked at 148 in the world.
She will face fellow American Christina McHale for a place in the last 32.
"My mom was up there in the Royal Box, so that was nice," said the American star after giving mother Oracene Price an afternoon to remember on Centre Court.
Williams claimed victory over Sadikovic on a second match point courtesy of a successful Hawk-Eye challenge .
"I never underestimate any opponent. I always expect the best of myself," added Williams, who won 12 straight points at the start of the match to open a 3-0 lead.
However, not everyone gave her the royal seal of approval.
"It was one of the worst serving efforts I've seen from Serena. This is what is giving other players hope," said US legend John McEnroe, commentating for the BBC.
Top seed Williams won her 21st major at the All England Club 12 months ago by beating Garbine Muguruza.
But her hopes of going level with Steffi Graf's Open era record of 22 have stalled since that day.
She went down to a US Open semi-final loss to Italy's Roberta Vinci followed by defeat in the Australian Open final to Angelique Kerber and then to Muguruza in the French Open final earlier this month.
Swiss fourth seed Stan Wawrinka defeated American teenager Taylor Fritz 7-6 (7/4), 6-1, 6-7 (2/7), 6-4 to set-up a second round blockbuster against Juan Martindel Potro.
Injury-plagued del Potro, a former US Open champion, is playing in his first Grand Slam event since the 2014 Australian Open after undergoing three wrist surgeries.
Del Potro made the second round by beating France's Stephane Robert 6-1, 7-5, 6-0.
The Argentina star is ranked at 165 but made the semi-finals at Wimbledon in 2013, while Wawrinka has twice been a quarter-finalist.
Nick Kyrgios, the Australian 15th seed, beat Czech wildcard Radek Stepanek, the oldest man in the draw at 37, in four sets, 6-4, 6-3, 6-7 (9/11), 6-1.
He next faces German wildcard Dustin Brown who got past Dusan Lajovic of Serbia 4-6, 6-3, 3-6, 6-3, 6-4.
Both Kyrgios and Brown have been headline makers in the past at Wimbledon after beating Rafael Nadal in 2014 and 2015 respectively.
Kyrgios had mid-match fallout with chair umpire Mohamed Lahyani and even told his own entourage to get out of the court.
The match took place on the same Court Two where last year the 21-year-old was accused of 'tanking' a game against Richard Gasquet.
"The crowd likes the way I play here, I entertain. I'm comfortable here and they know the tennis I bring every day," said Kyrgios, who was warned for bad language by Lahyani.
Second up on Centre Court is Andy Murray, the world number two and 2013 champion who tackles compatriot Liam Broady.
Murray has lost the Australian and French Open finals to Novak Djokovic this year and has since rehired Ivan Lendl as coach.
The two worked together when the British world number two won Wimbledon in 2013 and the US Open the year before.
They celebrated their renewed partnership with Murray claiming a record fifth Queen's Club title on the eve of Wimbledon.
Broady, 22, is ranked 234 in the world. He has won just one match on the main tour in his career and that was at last year's Wimbledon.
Later Tuesday, two-time champion Petra Kvitova, the 10th seeded Czech, faces injury-plagued Sorana Cirstea of Romania.
Australia's Bernard Tomic, the 19th seed, plays experienced Fernando Verdasco of Spain.
Former runner-up Agnieszka Radwanska of Poland, the third seed, faces Ukraine's Kateryna Kozlova.