The former world number one made just a single break in the opening set that was enough to seal a 6-4 success.
She again found a way through her opponent's serve in the next and had the chance to serve it out in the 10th game.
However, Barthel saved a match point and went on to break back and level the second at 5-5.
The game then went to a tie-break where Wozniacki didn't let her small blip games earlier affect her, racing to a 7-2 victory in the breaker.
Wozniacki, 21, will face world number nine Serena Williams after the American came through comfortably against Anastasia Pavlyuchenkova in another of this evening's matches.