The aggressive Romanian was too strong for her Russian opponent and secured a 6-0 6-2 victory in just 57 minutes at Roland Garros.
Halep has only made round two once before in Paris, but is expected to go much further this year after a superb last 12 months or so.
Her haul of six WTA Tour titles last season – and the 2014 Doha crown – has lifted the 22-year-old to fourth in the world rankings, and she was in no mood to give world number 87 Kleybanova any cause for hope on Tuesday.
Halep’s power on the baseline was just too much for the Russian, whose sole break-point opportunity came at 6-0 5-0 down.
Kleybanova duly got on the board before then holding her serve for the first time in the match.
However, that was merely delaying the inevitable, and Halep eased through to a meeting with either Barbora Zahlavova Strycova or Heather Watson.
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