Bogomolov, 28, has been in the form of his life this season, with career-best third-round appearances at both Wimbledon and the US Open.
But Baghdatis, 26, once ranked eighth in the world, claimed victory in an hour and three quarters, firing six aces.
The former Australian Open finalist has had a career punctuated by injuries, and now stands 60th in the ATP world rankings.
Neither player faced a break point in the opening set, with Baghdatis coming through comfortably in the tiebreaker, before going on to win the match. He will face either Somdev Devvarman of India or Russian Mikhail Ledovskikh in the next round.
Russian seventh seed Dmitry Tursunov, playing for the first time in Malaysia, overcame Chile's Paul Capdeville 6-2, 2-6, 6-1.
The first-round contest, which took two and a quarter hours, saw the South American saving 10 of the 14 break points he faced.
Tursunov, 28, is looking to earn the seventh ATP trophy of his career.
Meanwhile, Belgian David Goffin won a confrontation between wild cards, as he eliminated Australian Matthew Ebden 6-4, 7-6 (7/4) for his second ATP victory of the season.
Goffin, 20, lost only seven points on serve in the opening set, breaking his opponent in the penultimate game. In the second, Ebden lost out in a tiebreaker. Goffin will face Tursunov in the next round.
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