The close result -- with just a 0.2 per cent share of the vote separating the two parties -- will make negotiations to form the next coalition government particularly fraught.
The Social Democrats led by 56-year-old former trade union boss Antti Rinne picked up 40 seats after campaigning on a ticket of fierce opposition to the austerity imposed by the previous centre-right government.
The Finns Party, which won 39 seats, meanwhile focused almost entirely on an anti-immigration agenda, under the leadership of hardline MEP Jussi Halla-aho, who also decried the "climate hysteria" of the other parties.
Sunday's result see the Finns Party more than double its presence in parliament, from 17 seats to at least 39, and regaining all of the ground it lost when more than half of Finns Party MPs fled the party in 2017 on the election of hardline leader Jussi Halla-aho.
During the campaign, most parties expressed strong reservations about sharing a government platform with Halla-aho's party, though stopped short of ruling it out entirely.
Finnish governments are typically a coalition of three or four parties who form the minimum 101-seat majority in parliament.
The Social Democrats' Antti Rinne has previously said his party would find it "very difficult" to enter a coalition with the Finns Party.
Meanwhile Petteri Orpo, leader of the conservative National Coalition, said his party was "ready to discuss" with Halla-aho.
Outgoing Prime Minister Juha Sipila said his Centre Party was the night's "biggest loser", blaming the "difficult economic decisions" his administration made in an attempt to rebalance the economy after a long slump.
Voter turnout looked set to come in around 72 per cent, higher than the 70.1 per cent who voted in 2015.
The current government's cuts to Finland's prized education system, and a tightening of unemployment benefit criteria, had provoked loud and widespread public opposition.
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