The Nationalists ousted Labour in the Western Isles, a key marginal that saw one of the hardest-fought campaigns of the election, and took four of the seven regional places in Glasgow.
The Lib Dems, Tories and the Scottish Greens took the other places, meaning Solidarity candidate Tommy Sheridan will not be returning to Holyrood.
The SNP held on to its Tayside North and Perth seats, meaning John Swinney and Roseanna Cunningham will return to the Scottish Parliament.
The party also took five of the seven places on the Central Scotland list, ousting Scottish Senior Citizens' Unity Party candidate John Swinburne and Scottish Socialist Carolyn Leckie, who were both MSPs in the previous parliament, and five of the seven seats in the South of Scotland list.
The Tories won Roxburgh and Berwickshire from the Lib Dems.
Ms Sturgeon told BBC Radio Scotland she believed the SNP was likely to be the biggest party in terms of the percentage of votes, but admitted it was difficult to predict whether this would translate into seats.
She added: "There's absolutely no doubt about who has lost the election. Labour have lost seats, they've lost votes and they're clearly a party that has been rejected by the Scottish public.
"We are polling extremely strongly, we're winning seats in areas we've never won before and it's very likely that for the first time ever we will have first-past-the-post representation in every major Scottish city."
Ms Sturgeon also backed calls for an inquiry into the polling problems.
"Clearly many people found it difficult to understand the way in which to fill in the ballot paper and it does raise questions about the wisdom of having two separate elections on the same day," she said.
The voting process has been suspended in several locations due to problems with electronic counting.
There have also been an unprecedented number of spoilt ballot papers in all areas.
In Airdrie and Shotts the number of spoilt ballots was 1,536 - 90 higher than the majority of Labour's Karen Whitefield.
There were 2,035 spoilt papers in Glasgow Shettleston, 1,850 in Glasgow Baillieston and 1,736 in the city's Anniesland constituency.
The first Holyrood seat to be declared was Motherwell and Wishaw.
It was held by Scottish Labour leader Jack McConnell, with a reduced majority of almost 6,000 over the SNP.
Jack McConnell won Motherwell and Wishaw
Labour's Pauline McNeill held Glasgow Kelvin where the Greens came third in the only first-past-the-post seat they contested.
Labour also took the crucial Strathkelvin and Bearsden seat in the West of Scotland from independent health campaigner Jean Turner.
David Whitton, who formerly worked as a spokesman for the late Donald Dewar, won with a 3,388 majority.
The SNP's Joe Fitzpatrick took Dundee West from Labour with a swing of 6.1% and Tricia Marwick took Central Fife from Christine May with a swing of 7.6%.
Bruce Crawford won Stirling for the SNP with a swing of 9.5% from Labour.
In Kilmarnock and Loudoun, Willie Coffey of the SNP took the seat from Labour's Margaret Jamieson.
The SNP took the Falkirk West seat which had previously been represented by the Independent Dennis Canavan, who retired before the election.
Labour's Allan Wilson became the first minister to lose his seat when the Nationalists claimed the Cunninghame North constituency.
Mr Wilson, the deputy enterprise minister, had had a majority of more than 3,000 in the previous election.
But this time round Kenneth Gibson won the seat for the SNP with a slender majority of 48.