Williams barely broke a sweat, dropping only five games in a match that lasted just over an hour.
It was the first time that the two had faced each other with the world number one and top seed coming through against the world number 104 in typically brutal fashion.
The 31-year-old American struggled with her serve throughout the match, making just 58% of her first serves and was broken 3 times by her Georgian opponent.
Although red-hot favourite, Williams is now in a stronger position with 2nd seed, and world number 23, Simona Halep retiring hurt in her match against Italy’s Flavia Pennetta.
WTA Bastad round two results
1-Serena Williams (U.S.) beat Anna Tatishvili (Georgia) 6-2 6-3
Flavia Pennetta (Italy) beat 2-Simona Halep (Romania) 4-6 7-5 2-0 (Halep retired)
Richel Hogenkamp (Netherlands) beat 6-Lesia Tsurenko (Ukraine) 6-1 2-6 6-3
WTA Bad Gastein round two results
2-Annika Beck (Germany) beat Mandy Minella (Luxembourg) 2-6 6-4 6-4
Yvonne Meusburger (Austria) beat 3-Irina Begu (Romania) 6-3 6-3
Elina Svitolina (Ukraine) beat 6-Chanelle Scheepers (South Africa) 7-5 1-6 6-1
Patricia Mayr-Achleitner (Austria) beat Petra Martic (Croatia) 6-4 6-4
Arantxa Rus (Netherlands) beat Estrella Cabeza Candela (Spain) 5-7 7-5 6-3