Australia's top woman gave up a break lead in each set of Monday's 7-5 6-4 loss to Wozniacki, who was playing in her second match since splitting with golfer Rory McIlroy.
It was Stosur's second disappointing grass court loss ahead of Wimbledon, after she lost to compatriot Casey Dellacqua in Birmingham last week.
Meanwhile top seed Agnieszka Radwanska lost to Anastasia Pavlyuchenkova in three sets.
It means Radwanska falls at the first hurdle in Eastbourne for a third year running, with Pavlyuchenkova securing her seventh win over a player in the top five.
Following defeats at the first attempt to Tsvetana Pironkova in 2012 and Jamie Hampton last year, Radwanska again started poorly at the WTA Premier grass-court event as she found herself a set down after 40 minutes.
While she hit back to level, Radwanska was unable to take advantage of seven double faults from her opponent in a marathon 64-minute final set as Pavlyuchenkova won through 6-4 3-6 7-6 (7-4).
Fifth seed Angelique Kerber avoided an upset to set up a second-round meeting with Alize Cornet after moving past Alison Riske in straight sets.
Kerber found herself 3-1 down after dropping serve in the fourth game but recovered to take the first on a tie-break before winning through 7-6 (8-6) 6-4.
Elena Vesnina needed just over an hour to get past Shuai Peng 6-3 6-4, with the Chinese left to rue missed break point chances.
Peng, ranked 60th in the world, won just one of six break points as Vesnina booked herself a second-round fixture against either Madison Keys or Jelena Jankovic.
Sloane Stephens won all five break points as she moved past Caroline Garcia of France 6-2 6-4, while Cornet was the last competitor through as she saw off Bojana Jovanovski.
The French world number 25 broke the Serb four times in total to win 6-3 6-2.