Haase broke Baghdatis's serve in the second game to go 4-1 up before claiming the first set. He led 4-2 in the second but was a bundle of nerves serving for the match as the final game went to 10 deuces.
The Dutchman eventually converted his sixth match point when Baghdatis returned into the net.
"He is a great player but it also gives you the chance to play great. Today, I didn't play the game he likes. He wasn't at his best and I took advantage," Haase said.
Chennai Open: Complete Coverage