Ukrainian Tsurenko made her Italian opponent work hard for almost two hours to claim a 7-6 (7/4) 6-4 in Uzbekistan's capital but missed out on the chance to play qualifier Risa Ozaki in the last 16.
The Japanese had a slightly easier time against Kateryna Koslova on her way to taking a 7-5 6-2 first-round win.
Top seed Bojana Jovanovski is safely through having ousted Kurumi Nara 6-4 6-3 and the Serbian world number 58 will meet either Misaki Doi or Evgeniya Rodina next.
Yvonne Meusberger of Austria is seeded third and needed three sets to progress to a match against either Nigina Abduraimova or Petra Cetkovska, claiming a 2-6 6-2 6-1 win over Hungary's Timea Babos.
Reigning champion Irina Camelia-Begu will play Arina Folts or Maria-Teresa Torro-Flor after beating Alexandra Panova 7-6 (8/6) 6-1.
There were also wins for fifth seed Alexandra Cadantu, Mandy Minella and Nadiya Kichenok, who beat Sabina Sharipova, Olga Puchkova and Eva Birnerova respectively.
Teenager Donna Vekic, who stunned the WTA Tour to reach last year's final as a 16-year-old, returned to Tashkent to beat Lyudmyla Kichenok.
The Croatian ousted Ukraine's Kichenok 6-3 6-2 in one hour and 22 minutes and, in Monday's remaining singles match, Belarus' Olga Govortsova beat Michaella Krajicek 7-5 2-6 6-1.