Wickmayer needed a tiebreak to take the first set.
However, a break sufficed for the 20-year-old from Flemish Brabant to see off Flipkens in the second set.
The match was the only the second official meeting between the two Flemings on the WTA circuit.
Last year, Wickmayer beat Flipkens in three sets 7-6 (7/1), 4-6, 6-1 in Luxembourg.
Yanina Wickmayer will take on the Russian Zvonareva in the next round.