The 16-year-old traded breaks with the 10th seed as their contest got off to an unusual start.
Wozniacki was quicker to find her form and raced into a 3-1 lead before winning three successive games to close out a dominant first set.
Vekic responded in the second, producing moments of quality to underline why the London-based starlet is regarded as a leading prospect in the women's game.
Temperatures approaching 40 degrees in the shade had a visible impact on the youngster as the second set progressed, with Wozniacki grinding out a break to move into pole position for the match.
The 10th seed was made to serve out the match by her stubborn opponent but she duly obliged to clinch a competitive encounter in straight sets.