The British No.2, who has dropped to 84th in the rankings after a poor start to the year, produced a dominant display to beat the second seed 7-5, 6-4.
Watson's clash with Wozniacki remained on serve for the first 10 games before the Brit broke and then served out the set.
Wozniacki broke early in the second but Watson hit back immediately, then picked up another game in the fifth before going on to serve out the match.
Konta earlier was beaten by world No.73 Flipkens in just over two hours.
The fourth seed fought back from the brink of defeat to take the second set but was blown away in the decider to lose 6-3, 6-7(2), 6-1.
Konta trailed 5-4 in the second but broke serve before easing through the tie-break. But Flipkens responded in style in the third set, racing into a 5-0 lead and securing victory with a comfortable hold of service.