Kanepi, who missed time while recovering from an Achilles injury, looked smooth in her 6-1, 6-1 rout of Polish wild card Sandra Zaniewska indoors at Spodek Arena.
The news wasn't as good for pair of other seeded players, however.
Fourth-seeded Julia Goerges of Germany was knocked off by 38-year-old American qualifier Jill Craybas 6-7 (5-7), 6-3, 4-1, while No. 5 Alize Cornet of France fell in an upset to Slovakian qualifier Anna Schmiedlova 6-3, 6-0.
Other winners in Tuesday's second day of action included Romanian Irina-Camelia Begu, who overcame France's Mathilde Johansson 5-7, 7-6 (7-5), 6-1, and Luxembourg's Mandy Minella, who rallied to defeat Serbia's Vesna Dolonc 3-6, 7-6 (7-4), 6-2.
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