Her exquisite cross-court passing shots brought gasps of admiration from the Centre Court crowd, but Williams' patchy service often let her down in the difficult swirling conditions.
Williams, a notoriously slow starter, level-pegged to 3-3 in the first set but then effortlessly stepped up a gear to break Srebotnik's service.
The Slovenian's resistance crumbled in the second set and it took Williams just over an hour to ease through to a smooth victory.
Fifth seed Lindsay Davenport of the United States also advanced easily, beating Rita Grande of Italy 6-3, 6-1.
She joined Argentina's Paola Suarez, who rallied to beat Bulgarian 12th seed Magdalena Maleeva 2-6, 6-2, 6-3 to set up a meeting with Slovenia's Maja Matevzic, who ousted 24th seed Magui Serna of Spain 4-6, 6-3, 6-4.
Uzbek Iroda Tulyaganova saw off Hungary's Petra Mandula 6-3, 6-4.
