Baghdatis hit nine aces and converted four of his eight break points to win his first match this season at the indoor tournament.
Baghdatis said ''I don't have many matches in my legs because I only played the Australian Open this year. Here I was lucky enough to get the wild card.''
He will next play Taro Daniel, who beat Denis Istomin 6-2, 6-2.
Also advancing to the second round was Alexander Zverev, who saved one match point to rally past Luca Vanni 6-7 (3), 6-4, 7-5. Next up against Zverev will be second-seeded Marin Cilic.