Baghdatis blows away Murray in Holland
The world number five and second seed subsided quickly after leading 3-0 in the opening set, losing the first-round match 6-4 6-1 in little more than an hour.
Murray, the Rotterdam winner two years ago, broke serve twice to march into an early lead but Baghdatis replied with three breaks of his own to take the first set and never looked back.
Murray, whose hopes of ending Britain's long wait for a men's Grand Slam champion were dashed by Novak Djokovic in the Australian Open final 10 days ago, capitulated in the second set as Baghdatis went through to face Spaniard Feliciano Lopez in the second round.
"This is something that can happen, my service was poor and I didn't move too well and then it's difficult on fast courts like these," Murray said.
"In the past I took some extra rest after a tough Grand Slam tournament but then I also sometimes played badly when I came back on court, so it is no excuse that I started here this week."
In second-round play, Austrian fifth seed Juergen Melzer was dispatched by big-serving Croatian Marin Cilic 6-2 6-4 but eighth seed Jo-Wilfried Tsonga avoided joining him through the exit door with a 4-6 6-4 6-4 defeat of fellow Frenchman Michael Llodra.
Djokovic was ruled out of the tournament with a shoulder injury, meaning Sweden's world number four Robin Soderling tops the draw. Soderling opened with an easy win against Dutchman Robin Haase.