The Cypriot needed a third-set tiebreak to overcome German Denis Gremelmayr late on Tuesday and was equally tested by Wang, who was cheered on by a crowd delighted to see a Chinese man competing with one of the world's top players.
Wang never gave an inch without a fight and exploited the world number nine's lapses of concentration to force a tiebreak in the first set and break Baghdatis early in the second.
Baghdatis, however, drew on the competitive spirit he so amply displayed in a five-set defeat to Andre Agassi at the U.S. Open two weeks ago to break back and then break the stubborn Wang's service again.
He finally secured the victory with a crosscourt winner after an hour and 39 minutes and will next face Thai Danai Udomchoke, who progressed when Croatia's seventh seed Ivo Karlovic retired while 6-2 3-1 down.
"It was a great match, Jimmy Wang played very well," said 21-year-old Baghdatis, who admitted he had been feeling the effects of the late night on Tuesday.
"I was pretty tired but I served pretty well and played smart to conserve energy. That was my goal for today and I went through."
Slovakia's Dominik Hrbaty was the first seed to reach the quarter-finals of the $500,000 tournament when he overcame a second-set implosion to beat Austrian Alexander Peya 6-1 2-6 6-0.
"It was a strange game. In the first set he made a lot of mistakes, in the second set I made the mistakes and he served better which gave him more confidence," said the fifth seed, who next faces Croatian fourth seed Mario Ancic, a 6-3 7-5 winner over Italy's Stefano Galvani.
Nikolay Davydenko played through jet lag to claim the last place in the second round with a 6-3 6-4 win over Dane Kenneth Carlsen in a match held over from Tuesday to allow the Russian more time to rest.
Just four days after losing to Roger Federer in the U.S. Open semi-finals, the second seed cruised through the encounter to set up a last-16 clash with Slovenian qualifier Luka Gregorc.
The world number five's accuracy gave Carlsen nothing to play with in the first set and when the journeyman Dane did break early in the second, the Russian merely changed his racket and broke back.
Facing three break points in the next game, Davydenko battled back to deuce before slamming the door in his 33-year-old opponent's face with a couple of aces.
"Yes, I feel a little bit tired," Davydenko said. "It's very nice that the organisers allowed me to move this match from yesterday evening to this morning. Yesterday I would have had no chance but today I felt like I could win."