Federer had his hometown crowd in a state of anxiety as he mistimed several forehands, lost his serve three times, and volleyed below his usual standards.
He repeatedly got out of trouble with aces, including one of his 11 to save a first set point when trailing 5-3.
Nieminen, who hadn't taken a set off Federer in nine previous matchups, also was two points from claiming the first set at 5-4 and in the tiebreaker. Ultimately, Federer won the set on a wide forehand by the left-handed Finn.
Federer squandered an early break in the second set but dominated the tiebreaker, finally winning when Nieminen netted an attempted pass after 96 minutes.
In Friday's quarterfinals, the top-seeded Swiss will play Simone Bolelli of Italy, who beat Marcel Granollers of Spain 6-4, 6-2.
Second-seeded David Nalbandian, the 2002 champion and twice runner-up, beat Kristof Vliegen of Belgium 6-4, 5-7, 7-6 (4) to also reach the quarterfinals.
He and Argentine countryman Juan Martin del Potro, are on course to meet for the second time in two weeks, in the semifinals.
Third-seeded del Potro made just four unforced errors as he cruised past Switzerland's Stephane Bohli 6-3, 6-3.
Fourth-seeded James Blake hit 18 aces as he came from behind to beat Oscar Hernandez of Spain 6-7 (4), 6-2, 6-4 to reach the last eight for the first time in three visits.
"I was serving well and that got me out of a lot of trouble,'' Blake said.
Usain Bolt Is A Blanco
Federer needs three sets to beat Reynolds
