Gasquet lined up in Rotterdam as the fourth seed, having already won two tour titles this season and boasting an unbeaten record apart from a defeat to compatriot Jo-Wilfried Tsonga at the Australian Open.
But the World No 10 never got going against Cypriot Baghdatis, who had also beaten him at the London Olympics last year.
“Richard was probably tired, he’s played a lot of tennis this season,” said Baghdatis.
“He was not at his best and tired from last week,” he added, in reference to Gasquet’s run to victory in Montpellier.
Spotted: Twinkle Khanna, Shriya Saran at an event in Mumbai
Andrew Flintoff's birthday: 10 players who entered different sports
Photos: Ranveer Singh and Vaani Kapoor go 'Befikre'
Photos: Aishwarya, Sridevi, Karisma at Manish Malhotra's birthday bash
Photos: Salman Khan, Shah Rukh Khan, other celebs at Star Screen Awards