The Czech star continues her fine 2021 form, beating World No.2 Osaka in three sets.
The three-time champion Kvitova edges past the German to reach the third round in Madrid.
Barty overcomes Tamara Zidansek in three sets, while Swiatek eases past Laura Siegemund in straight sets.
Pliskova rallied from a set down to beat Gauff; No.11 seed Jennifer Brady had it easy against Venus Williams.
The 27-year-old is eager to get back to his best when he returns to action in Madrid Open.
Djokovic, who has only played four tournaments this year, suffered a surprise defeat to Aslan Karatsev in semifinals of the Serbia Open last week
Along with Federer, Novak Djokovic and Rafael Nadal are also on the star-studded entry list of the next month's Madrid Open