Wozniacki, who will be top seed at Flushing Meadows in lieu of injured world number one Serena Williams, has been in superb form on the North American hardcourts and arrived in New Haven after her victory at the Montreal Cup earlier this week.
Despite being forced to play a semi-final and final at the rain-hit Montreal event on Monday, the 20-year-old Dane appeared fresh and needed just over 80 minutes to set up a quarter-final meeting with Flavia Pennetta.
The seventh seeded Italian also advanced easily, brushing past Olga Govortsova of Belarus 6-3 6-2.
Russian fourth seed Elena Dementieva had to battle her way into the last eight with a tough 7-6 6-7 6-4 win over Ukraine's Kateryna Bondarenko while sixth-seeded Frenchwoman Marion Bartoli crushed Australia's Anastasia Rodionova 6-3 6-1.
Baghdatis had problems with his serve in the opening dropping all three of his service games, but the Cypriot recovered to break Chela's serve four times over the final two sets.
James Blake's troubles continued as the American surrendered meekly to seventh seed Alexandr Dolgopolov of Ukraine 6-4 6-2.
(Writing by Steve Keating in Toronto; editing by Ian Ransom)