Cheered on at the Finals in Malaga by thousands of Finnish fans who have made the nearby town of Fuengirola their home, the tournament outsiders prevailed 2-1 with Otto Virtanen and Harri Heliovaara securing a famous victory in the doubles decider.
Finland boasts famous figures in Formula One, ice hockey, athletics and winter sports but not many noted tennis players and former world number 13 Nieminen said his team's best-ever Davis Cup run could inspire a new generation.
"Many people play tennis. Not so many compete," Nieminen told reporters. "We don't have too many professional players. It's a popular hobby sport, but not one of the traditional sports in Finland.
"Now tennis is getting bigger and bigger. Even before our success, tennis was getting a little bit bigger. Now tennis is getting more attention. The Davis Cup team is getting more attention.
"Just that you're able to see more tennis on TV or in the newspapers helps and you have idols like these guys. It's not one of the biggest sports but hopefully it will be in the near future."
Finland will play the winner of Wednesday's quarter-final between 2022 runners-up Australia and the Czech Republic in Friday's semi-final.
"We have the belief that we have high goals, but it doesn't help to expect that everything always goes well," Nieminen said.
"We always try to work hard. We obviously expect more great experiences on Friday."
