Voegele went on to register an easy 6-3 6-2 win over another Lucky Loser Polona Hercog.
Voegele will play compatriot Belinda Bencic on Tuesday for a place in the third round.
Meanwhile, Arruabarrena, the world number 90, stunned Cibulkova in the first set by overcoming a 5-1 deficit to get back on serve.
The Spaniard eventually won the first set against a player looking for her first win of the season.
But Cibulkova regained her rhythm, losing only three games in the next two sets.
"It's my first win of 2019. So I am pretty pleased that I finally won my first match of the year. It wasn't easy, you know, because Lara is always a tough opponent," the 29-year-old Cibulkova said.
The Slovakian player then revealed why she lost her momentum in the first set, despite enjoying a commanding 5-1 lead.
"Maybe, I lost my concentration a little bit. And also she played some good points. Sometimes these things happen in tennis. But I don't want that to happen in the next round," she said.
Cibulkova, though, cannot afford to take her foot off the gas against Australian Open semifinalist Pliskova -- also a former Dubai runner-up -- in the next round.
"Yes, it's going to be a tough match. I am looking forward to it and I will just do my best," she said.
Earlier, Elise Mertens, the 16th seeded Belgian, lost to Chinese qualifier Lin Zhu 5-7 6-4 7-5 in the first round.
On what was a memorable day for the qualifiers, Jelena Ostapenko, the 2017 French Open champion, lost in straight sets (6-4 6-0) to American qualifier Jennifer Brady.
Brady will face Garcia in the second round on Tuesday.
Meanwhile, Julia Goerges, the 13th seed who was a runner-up in Dubai in 2012, lost in straight sets (6-4 7-5) to American Alison Riske who will take on Alize Cornet of France in the second round.
Fifteenth seed Anett Kontaveit of Estonia also lost her first round match to Shuai Zhang of China (7-6 6-3).Results
Ons Jabeur (Tunisia) beat Donna Vekic (Croatia) 6-4 7-6 (11/9)
(LL) Dalila Jakupovic (Slovenia) beat (LL) Zarina Diyas (Kazaksthan) 1-6 6-1 6-2
Alison Riske (USA) beat (13) Julia Goerges (Germany) 6-4 7-5
(Q) Jennifer Brady (USA) beat Jelena Ostapenko (Latvia) 6-4 6-0
(Q) Lin Zhu (China) beat (16) Elise Mertens (Belgium) 5-7 6-4 7-5
Sofia Kenin (USA) beat Mihaela Buzarnescu (Romania) 6-3 6-0
Katerina Siniakova (Czech Republic) beat Petra Martic (Croatia) 6-4 6-3
Carla Suarez-Navarro (Spain) beat Barbora Strycova (Czech Republic) 6-1 6-3
Shuai Zhang (China) beat (15) Anett Kontaveit (Estonia) 7-6 (7/3) 6-3
Dominika Cibulkova (Slovakia) beat (Q) Lara Arruabarrena (Spain) 5-7 6-1 6-2
(LL) Stefanie Voegele (Switzerland) beat (LL) Polona Hercog (Slovenia) 6-3 6-2
(14) Caroline Garcia (France) beat Anastasia Pavlyuchenkova (Russia) 6-2 6-0
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