The second seed saw off her 44th-ranked Czech compatriot 6-7 (3/7), 6-4, 6-4 in over two-and-a half hours at the Aviation Club.
The Wimbledon champion in 2011 and 2014 said she was unfazed about the early start.
"I don't really care if I play the first match," the WTA number four said. "Now I'm done, so I have a free afternoon."
"I''m not sure what I'm pleased with... maybe with my comeback at the end.
"Even when I lost the tiebreak, I was really fighting in the first set to get it done, then the tiebreak was just a little bad from my side.
"I won my first two games in the second set. It was really helpful for me mentally. That's probably what I'm pleased with."
Kvitova missed the Gulf event a year ago with injury and won the title in 2013.
Taiwan's Hsieh Su-Wei defeated Belarus Aliaksandra Sasnovich 6-1, 6-2 while Victoria Kuzmova accounted for seventh seed Kiki Bertens, beating this month's St Petersburg champion 6-2, 4-6, 7-6 (8/6).
American Sofia Kenin, winner of last month's Hobart title, defeated Russian 11th seed Daria Kasatkina 6-3, 2-6, 6-4. Alison Risk of the US also advanced with a 6-2, 6-3 win over France's Alizé Cornet 6-2, 6-3.
Local favourite Ons Jabeur was forced to retire with the Tunisian trailing two-time tournament champion Eliva Svitolina 7-6 (7/4), 4-0.
The challenger took a fall late in the opening set, potentially rolling her ankle while also hitting her shoulder. She took a medical timeout out but was able to carry on in the second set for just a handful of games.
Sviolina is on a hot streak in the emirate, winning the last two editions and her last 10 Dubai matches.
The third seed is hoping to become the first women to win three editions.
"That is a big motivation for me here," the Ukrainian said. "Today I didn't really feel in a match mood, I don't know why.
"I was struggling a bit, I had a very slow start. Hopefully tomorrow will be better.
"I told myself that I'm here to make history of the tournament."
Results from the WTA tournament in Dubai on Tuesday (x indicates seeding):
Petra Kvitova (CZE x2) bt Katerina Siniakova (CZE) 6-7 (3/7), 6-4, 6-4
Hsieh Su-Wei (TPE) bt Aliaksandra Sasnovich (BLR) 6-1, 6-2
Viktoria Kuzmova (SVK) bt Kiki Bertens (NED x7) 6-2, 4-6, 7-6 (8/6)
Sofia Kenin (USA) bt Daria Kasatkina (RUS x11) 6-3, 2-6, 6-4
Alison Riske (USA) bt Alize Cornet (FRA) 6-2, 6-3
Elina Svitolina (UKR x6) bt Ons Jabeur (TUN) 7-6 (7/4), 4-0 - retired
Carla Suarez Navarro (ESP) bt Zhang Shuai (CHN) 6-4, 6-4
Belinda Bencic (SUI) bt Stefanie Voegele (SUI) 6-1, 6-1
Garbine Muguruza (ESP x12) bt Zheng Saisai (CHN) 7-5, 6-2
Jennifer Brady (USA) bt Caroline Garcia (FRA x14) 6-4, 7-5
Simona Halep (ROM x3) bt Eugenie Bouchard (CAN) 7-6 (7/4), 6-4
Angelique Kerber (GER x5) bt Dalila Jakupovic (SLO) 7-6 (7/4), 6-3
Lesia Tsurenko (UKR) bt Lin Zhu (CHN) 6-4, 6-7 (5/7), 6-3
Kristina Mladenovic (FRA) bt Naomi Osaka (JPN x1) 6-3, 6-3
Aryna Sabalenka (BLR x8) bt Ivana Jorovic (SRB) 6-4, 6-0
Karolina Pliskova (CZE x4) bt Dominika Cibulkova (SVK) 6-2, 3-6, 6-3