The second seed produced a comprehensive display at the WTA International event and only needed 83 minutes to record a 6-2 6-4 first-round win in Azerbaijan.
Svitolina made a solid start to the hard-court season with a quarter-final appearance in Istanbul last week and maintained that form in the opening set to win 50 per cent of points on Abduraimova's serve and break at every attempt.
It was not until the eighth game of a much calmer second set, on Svitolina's serve, that the first opening arrived.
That was saved and the world number 37 promptly hit back before serving out to victory at the sixth attempt.
She will be joined in the second round by top seed Sorana Cirstea, but three other seeds were sent tumbling out of the competition.
Cirstea only dropped 31 points on her own serve against Ons Jabeur and wrapped up a 6-3 6-3 win in just under 90 minutes.
The Romanian won six consecutive games to take the opening set and build up a 2-0 in the second and, with Jabeur only holding serve once in the final set, Cirstea's progress was assured.
Magdalena Rybarikova, Kurumi Nara and Heather Watson had less productive days, though, as they all exited the competition to players outside the top 70.
World number 183 Misa Eguchi made the second round of a WTA event for the first time with a 6-4 7-6 (9-7) win over third seed Rybarikova, while Francesca Schiavone became the second Italian in a week to beat Kurumi Nara after Roberta Vinci did the same in Istanbul.
Seventh seed Watson reacted well after the losing the first set against Kristina Mladenovic, only to lose 72 per cent of points in the decider as she was beaten 6-2 3-6 6-0.
Julia Glushko needed three sets to edge past Kateryna Bondarenko and there were straight-set wins for Vesna Dolonc, Donna Vekic, Silvia Soler-Espinosa and eighth seed Jana Cepelova.
The Slovakian set up a second-round tie with Pauline Parmentier with a 6-1 6-0 win over Nazrin Jafarova and only dropped 15 points on the way through.