The top seed was never in trouble, despite her opponent winning three straight games in the second set, as she ran out a 6-2 6-3 winner to line-up a last-eight meeting with fifth seed Lourdes Dominguez Lino.
The win over Tatishvili means Williams has a record of 25 wins and no losses on clay this year and she revealed she is approaching the tournament like a grand slam event.
"I've had a lot of time here but I've actually been spending a lot of time in the room, just staying focused on the event," Williams told wtatennis.com.
"My main goal is to do well here. I love this city, but I really love the fans, and I feel like I want to do the best that I can here. I'm staying really focused, grand slam style.
"You never want to go to a tournament and not win, or at least not perform your best. I don't know if I'll end up winning the tournament this week, but I want to play some of my best tennis here."
Number two seed Simona Halep saw her competition end due to a retirement as a lower back injury forced her to pull out of her match against Flavia Pennetta when the score was 4-6 7-5 2-0. Pennetta will now play Virginie Razzano in the quarter-finals.
Qualifier Richel Hogenkamp saw off the challenge of sixth seed Lesia Tsurenko to win 6-1 2-6 6-3 today while Mathilde Johansson also came through her second round match, beating Andrea Gamiz 7-5 6-2.