Berankis beat Istomin 6-2, 6-2 at the Nice Lawn Tennis Club, advancing to Round 2, where he will take on Edouard Roger-Vasselin.
The French wild card moved on when his opponent, Colombian Alejandro Falla, left with a calf injury after losing the first set 7-5.
Spain's Nicolas Almagro is seeking his third straight title at this year's Nice event.
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