Isner converted his second match point against the unseeded qualifier to triumph 4-6 6-2 7-5 in one hour, 43 minutes.
The later semi-final was even closer, and longer, as fifth seed Baghdatis edged seventh seed Gilles Muller, of Luxembourg, 6-7(4) 6-3 7-6(4) in their finely balanced match.
Baghdatis served for the match at 6-5 in the third set, only to tighten up and allow Muller to force a deciding tie-break.
"At 6-5, I have to be honest, I choked but I was able to keep calm and find a way in the end and I’m very happy about that," Baghdatis told ESPN after winning every service point in the tie-break.
A losing finalist at the 2006 Australian Open, he has four ATP titles but has not won a tournament since 2010 and will need to be near his best in his first final since 2011 to beat fellow 30-year-old Isner, against whom his career record is 0-5.
Isner, who also dropped the first set in his semi-final, said a more aggressive approach to returning serve in the second set had been the key to victory.
"That 2-1 game in the second set turned the match around," Isner said. "My shots found the court, I was able to break and it relaxed me a lot from there.
"When I'm up a break I tend to serve my best because most of the time when I get one break I can take that set home."
(Reporting by Andrew Both, editing by Tony Jimenez/Greg Stutchbury)
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