Gibbs double-faulted on her first serve and then seemed to regain her composure and played a number of strong points the rest of the way.
Williams, who credited her win at Stanford last year as rejuvenating her career, said it took some time to adjust to the different conditions between Wimbledon grass and California hard court.
In other matches, fifth-seeded Yanina Wickmayer of Belgian beat Heather Watson of Britain 5-7, 6-1, 6-4 and sixth-seeded Chanelle Scheepers of South Africa topped wild card Michelle Larcher De Brito of Portugal 6-3, 6-4.