Four days after losing in the women's doubles semifinals at the U.S. Open, the Czech Republic native experienced a much enjoyable outing against Tatishvili. Safarova needed only 45 minutes to advance and recorded nine aces while also dominating in other areas.
She converted 89 percent of first service points, 80 percent on second service points and 75 percent of break points. Those totals allowed Safarova to win 72 percent of the possible points in the match.
Safarova will next face unseeded American Sofia Kenin, who advanced with a 5-7, 6-4, 6-3 win over Tereza Martincova of the Czech Republic.
Safarova was the highest seed in action on Tuesday, but it was not a perfect day for seeded players.
Unseeded Canadian Bianca Andreescu recorded a 6-3, 6-2 victory over sixth-seeded American Jennifer Brady. Andreescu dominated the match from the outset, won 79 percent of first service points and completed the match in 61 minutes.
Andreescu will next face Lucie Hradecka, who coasted to a 6-1, 6-3 win over fellow Czech player Andrea Hlavackova.
Fourth-seeded Tatjana Maria of Germany and seventh-seeded Alison Van Uytvanck of Belgium both needed to win tiebreakers to advance.
Maria recorded a 6-2, 7-6 (4) win over Fanny Stollar of Hungary, while Van Uytvanck beat Carol Zhao of Canada 6-4, 2-6, 7-6 (1).
Maria next will face American Grace Min, while Van Uytvanck opposes Australian Marina Erakovic.
In the other matches Tuesday, Sachia Vickery beat Taylor Townsend 7-5, 6-0 in a battle of two Americans, and eighth-seeded Viktorija Golubic of Switzerland topped the Czech Republic's Barbora Krejcikova 7-5, 6-4.