The seven-times champion, who has struggled with a knee injury this year, showed no ill effects as she beat Giulia Gatto-Monticone 6-2 7-5.
Williams, who also has a doubles date with Andy Murray at SW19, said: "I haven't played a ton of matches. I think this is the 13th match for the whole year for me.
"It felt really good to get there. It's also Wimbledon. It's Centre Court. It's like such a big moment for me.
"I haven't felt this good in months, almost five months. I know my body really well. I know my limits. If something is off, I'll know that it's off.
"But so far I literally haven't felt like this since February. It's a really good feeling."
Angelique Kerber, who beat Williams in last year's final, started the defence of her title with a comfortable victory over Tatjana Maria.
Kicking off the action on Centre Court on day two, the German eased to a 6-4 6-3 win over her compatriot in front of the watching Duchess of Cambridge in the Royal Box.
Despite not winning a tournament since last year's triumph, Kerber has shown some good recent form, including reaching the final in Eastbourne last week.
And the 31-year-old, who lost her only previous meeting with Maria, avoided becoming the first ladies' champion to be defeated in the first round the following year since Steffi Graf in 1994.
Kerber said: "I was really nervous, to be honest, because of course going out there as the defending champion, it was really special.
"Walking on the Centre Court, playing there again, I mean, a lot of emotions, a lot of memories.
"But I was enjoying this. I was really enjoying the match. I was enjoying the points and the crowd. It was a really nice match, but of course with a lot of nerves at the beginning."
French Open champion and new world number one Ashleigh Barty eased into the second round courtesy of a 6-4 6-2 victory over Saisai Zheng.
Two-time winner Petra Kvitova beat Ons Jabeur 6-4 6-2 and British number one Johanna Konta secured a 7-5 6-2 win over Romanian qualifier Ana Bogdan.
Former champion Garbine Muguruza was the victim of a big shock as she was beaten in straight sets by Brazilian Beatriz Haddad Maia.
The 2015 winner and former world number one, who has fallen down the rankings in the last two years, lost 6-4 6-4.
Maria Sharapova, winner in 2004, bowed out after retiring at 5-0 down in the final set against Pauline Parmentier due to a wrist injury.