The fifth-seed took just 23 minutes to take the first set but the second was a totally different affair as the Czech proved why she broke into the world’s top 100 for the first time earlier this season.
Wozniacki will next face 31st seed Camilla Giorgi, who beat Spain’s Lara Arruabarrena in very similar fashion, 6-0 7-6.
Allertova, 22, was making her Wimbledon debut and initially looked out of her depth facing the world No 5 on the 1,000-capacity Court 12 in only her second tour-level match on grass.
Wozniacki raced into a 5-0 first set lead but Allertova escaped the tennis players’ dreaded ‘bagel’ by finally winning a game on serve.
However, Allertova looked a different player in the 63-minute second set, throwing in drop shots and hitting winners before Wozniacki, a two-time US Open finalist, came out best in the tie-break.