"I served a lot better than I did in my last two matches," said Murray, the No. 1 player in his transplanted England. "My serve is an area I've worked a lot on since coming back from (the Australian Open)."
Elsewhere, Croat Mario Ancic topped Sweden's Robin Soderling, a former Marseilles finalist 6-3, 6-7 (4-7), 6-2; and eighth-seeded Frenchman Paul-Henri Mathieu was beaten by unseeded compatriot Gilles Simon 6-3, 6-4.
Saturday's semifinals pit Murray against Mathieu and Ancic against Baghdatis.
The eventual champion will collect $125,000 on Sunday.