The 16-time Grand Slam champion broke four times in the first set and twice in the second at the clay-court tournament. She had seven aces, while her opponent served nine double-faults. Williams ousted Tatishvili in the first round of the French Open in May.
The top-seeded Williams will face Lourdes Dominguez Lino on Friday.
Flavia Pennetta advanced when second-seeded Simona Halep of Romania retired with an undisclosed injury. The Italian was leading 4-6, 7-5, 2-0 at the time.
Also in the second round, Richel Hogenkamp beat Lesia Tsurenko 6-1, 2-6, 6-3.