Konta, the world number eight who will carry Britain's hopes into Wimbledon along with Andy Murray, won 6-4 6-1 against the Belgian Wickmayer and will face Australian Ashleigh Barty next.
Konta, surprisingly beaten in the French Open first round by world number 109 Hsieh Su-Wei, coped better with Nottingham's windy conditions as she forged 4-0 ahead in the opening set.
Wickmayer briefly threatened to make a match of it but Konta was relatively untroubled.
"I was able to deal with the conditions well. I really enjoy playing in front of this home crowd," she said.
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(Reporting by Martyn Herman; editing by Mark Heinrich)
