The five-times champion looked supremely comfortable on the Centre Court lawn, dispatching powerful groundstrokes down both flanks and thumping 16 aces past her 113th-ranked opponent, including four in the sixth game of the second set.
Top seed Williams, beaten by Spain's Garbine Muguruza in the second round at Roland Garros, ensured Tatishvili's suffering lasted only 61 minutes, rattling off five games in a row in the second set for the match.
She joins sister Venus in the second round where set will meet Chanelle Scheepers of South Africa or American Christina McHale.
(Reporting By Clare Lovell, editing by Pritha Sarkar)
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