Lleyton Hewitt's team, who lost to Canada in the 2022 final and missed the opportunity to close in on 32-time champions the United States, will face Serbia or Italy who meet in the second semi-final on Saturday.
Giant-killers Finland were the only country left in Malaga to have not won a Davis Cup crown after the Netherlands lost to Italy but their quest to make a first final in the elite men's team competition ended with a whimper.
De Minaur, who sparked Australia's comeback victory in their quarter-final against the Czech Republic, left the Finns with an uphill task as he showed his resolve to recover from an early break against Ruusuvuori and take the first set.
Ruusuvuori showed little sign of the shoulder problem that kept him out of Finland's stunning win over champions Canada in the last eight and played aggressively in the second set but De Minaur held firm.
"Extremely proud moment but I could have not done it without these guys," De Minaur said, pointing to his team.
"What we have been able to accomplish in back-to-back years is special just to show we come together as a group and how important it is for us.
"Alexei hasn't played for Australia in a very long time and had a massive match. He played a very high-quality opponent and dug super deep. He won us the tie.
"I'm happy to be in another final and hopefully we can do one better."
BLISTERING GROUNDSTROKES
World number 171 Virtanen earlier served with venom and let rip a blistering array of groundstrokes in a tight first set but came unstuck towards the end, as Popyrin saved a set point and pounced in the tiebreak.
Popyrin, a late replacement for the injured Thanasi Kokkinakis, grabbed the first break in the second set when Virtanen hit two successive double faults as Australia sensed an opportunity.
The 40th-ranked Popyrin closed out the win and silenced a huge crowd of boisterous Finnish supporters who have made the nearby town of Fuengirola their home.
"I think the majority of the fans were Finnish, apart from our little corner that we had behind the bench," Popyrin said.
"It's nerves that I've never experienced before in my life, the nerves playing the first tie, the first rubber of a Davis Cup, winning my first live rubber of a Davis Cup.
"I just had to keep my head steady and really focus on my serve and try to capitalise on opportunities when they came."
De Minaur said Australia would be tricky opponents for any team in the final and tipped the doubles duo of Matthew Ebden and Max Purcell to play a vital role.
"No team really wants to play us," De Minaur added.
"We're a solid squad. We've got a lot of depth in every position. If we get ourselves to a doubles we've got an unbelievable pairing."
