After falling behind 1-3 in the first set on Day 1, the world No. 1 great responded by winning 11 of the next 13 games in a 6-4, 6-1 victory over little-known Russian Margarita Gasparyan at the venerable All England Club.
The reigning French and Aussie champion Williams is seeking a sixth Wimbledon title and her first since 2012. The American is also a two-time runner-up at the AEC.
Williams' second-round opponent will be Hungarian Timea Babos.
Eleventh-seeded Czech slugger Karolina Pliskova held off American Irina Falconi 6-4, 4-6, 6-1, while 23rd-seeded former No. 1 Victoria Azarenka drilled Estonian Anett Kontaveit 6-2, 6-1.
Kazakhstan's Zarina Diyas dismissed 24th-seeded Italian Flavia Pennetta 6-3, 2-6, 6-4.
Czech Petra Kvitova captured her second Wimbledon title in four years by beating Canada's Genie Bouchard in last year's lopsided finale.