The Serb, seeded 10th for the WTA Premier grass-court tournament in Birmingham, was among the first competitors to crash out as she came unstuck against Wickmayer for a fourth time in her career.
The world number 54 maintained her 100 per cent record against Jovanovski, saving five of seven break points to win through 6-4 6-4.
Unlike Jovanovski, there was no such early exit for Shuai Zhang as she came through a hard-fought meeting with Eleni Daniilidou victorious.
The pair were separated by 309 places in the rankings prior to their first meeting and, despite Daniilidou pushing the ninth seed much of the way, she fell short in a 7-5 6-4 defeat.
She is joined in the next round by Madison Keys as she saw off Teliana Pereira of Brazil in just over an hour, with fellow Americans Coco Vandeweghe and Varvara Lepchenko enjoying straight-set victories over Zarina Diyas and Alison Van Uytanck respectively.
Away from the seeded players, Karolina Pliskova suffered a surprise exit as she was beaten by France's Virginie Razzano.
The 31-year-old Razzano, who formerly occupied a world ranking of 16, now resides outside the top 100, but came through against the Czech, ranked 56 places above her, in just over an hour and a half.
There will be no repeat of last year's heroics for 2013 finalist Donna Vekic as she was beaten 6-4 6-4 by Belinda Bencic of Switzerland.
Vekic lost out to Daniela Hantuchova last year and Bencic will face the Slovak world number 31 next, while Kimiko Date-Krumm won 81 per cent of her first service points to brush aside Argentina's Paula Ormaechea 6-3 6-1 in less than an hour.
Francesca Schiavone will face third seed Sloane Stephens in the second round after her 6-3 6-4 triumph over Jie Zheng although her French Open adversary Ajla Tomljanovic crashed out.
The Croatian came out on top in their Roland Garros first-round meeting before reaching the last 16, but the 21-year-old was beaten 6-1 6-4 by Mona Barthel of Germany. There were mixed emotions for the Kichenok sisters - Nadiya beating Sharon Fichman and Lyudmyla losing out to 15th seed Alison Riske.
America's Lauren Davis was on court for almost two hours before beating Tamira Paszek prior to compatriot Victoria Duval seeing off 13th seed Carolina Garcia of France 6-2 6-4.
Shahar Peer and Camila Giorgi were also late winners as they edged Kristina Mladenovic and Katy Dunne respectively.