WATCH the WTA Tour LIVE on beIN SPORTS | via Foxtel, Kayo, Fetch & beIN SPORTS CONNECT
Top seed Kontaveit overcame world number 61 Irina Bara in straight sets in her first-round clash and third favourite Krejcikova followed suit in her second-round match against Poland's Magdalena Frech.
Kontaveit will meet Sweden's Rebecca Peterson in the next round as she looks to set up a quarter-final meeting in Germany with eighth seed Andrea Petkovic, who defeated Misaki Doi 6-4 6-3 on Wednesday (AEST).
There was no such luck for ninth seed Elena Gabriela Ruse, though, after she lost 6-0 6-4 to last week's Budapest Grand Prix winner Bernarda Pera.
Swiss Joanne Zuger will next be the next challenge for Pera as she aims to reach a quarter-final clash against Katerina Siniakova, who triumphed 6-1 6-1 over Brazil's Laura Pigossi.
Putintseva is ranked as the second favourite in Italy and progressed with ease from her first-round clash against world number 147 Jaimee Fourlis, winning 6-3 6-1.
Seventh seed Anna Bondar had little difficulty beating Clara Burel 6-4 6-4, though Caroline Garcia and Nuria Parrizas Diaz faced more difficult tasks in their respective openers.
France's Garcia, the fifth favourite in Palermo, responded to a first-set scare to defeat compatriot Chloe Paquet, while eighth seed Parrizas Diaz also lost her opening set before downing Asia Muhammad.
