The 47th-ranked German will face a huge test Sunday when he goes in as underdog against either Roger Federer or Ivan Ljubicic.
Victory in two and a quarter hours gave Mayer another chance to lift the first trophy of his career.
Nieminen, a Stockholm finalist in 2001 and 2006, missed in a decisive third-set tiebreaker as Mayer put over a cross-court winner which the 29-year-old Finn could not reach on the first of three match points.
The Finn came to the court with a 4-2 lead in the series and had won 11 of his 13 matches since a first-round US Open loss.
Mayer said he goes into the title match facing a huge deficit. "I have nothing to lose. I was a little tired today, physically and mentally.
"But I fought hard, I played for the line on match point and had a bit of luck. After losing the second set I was able to come back in the third."
Mayer, who defeated sixth seed Feliciano Lopez in the first round and Swedish number five Robin Soderling in the Friday quarter-finals, won his 23rd match of the season as he played in only his second semi-final of 2010.
"I didn't play my best today but I fought unbelievable out there. I really wanted to be in the final. I think I deserve it."
Mayer's win was only his third on hardcourts this season against 12 defeats on the surface.