The top-seeded German had lost two of three encounters with the big-hitting Begu last year and was 2-2 overall against the Romanian in career head-to-head meetings.
"I was trying to focus on myself because it's always tough to play against her. Sometimes you lose your rhythm against her, so that's what I was focussing on," Kerber said in an on-court interview.
"Just trying to go for it, move good on clay and just win the match because I remember the last match against her, I lost!" added the German, who fell to Begu on clay in Rome after losing to her at the 2015 Australian Open.
Begu did not appear to be at her best following a difficult Round of 16 clash against Monica Puig which was decided by a third set tie-break under the lights on Thursday.
The Romanian was loose with her groundstrokes, amassing 35 unforced errors to only nine by Kerber, who did not face a single break point in the 72-minute match.
Later quarter-finals have fifth-seeded Italian Sara Errani facing Yulia Putintseva of Kazakhstan, and Laura Siegemund of Germany taking on Russian Elena Vesnina.
(Reporting by Larry Fine in New York; Editing by Mark Lamport-Stokes)
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