Yesterday with 59 constituencies in Scotland declared, the SNP had picked up an unprecedented 56 seats. The three remaining seats went to the LibDems, Labour and the Conservatives.
The party's best ever result previously had been in October 1974, when 11 SNP MPs were returned to the House of Commons.
Sturgeon said the dramatic collapse in Labour support was due to the party "losing the trust of the people of Scotland".
In Glasgow, a former Labour stronghold, all seven seats were won by the SNP.
Sturgeon said: "What we're seeing tonight is Scotland voting to put its trust in the SNP to make Scotland's voice heard, a clear voice for an end to austerity, better public services and more progressive politics at Westminster. That's what we now intend to do.
"I hope we're not looking at another Conservative government, but if we are then it will be more important that there are strong SNP MPs in Westminster, making Scotland's voice heard and making sure Scotland's interests are protected."
Responding to an incredible evening for the SNP, famously optimistic former party leader Alex Salmond admitted that even he hadn't predicted such a huge swing in their favour.
The winds are blowing across Scotland and they're blowing very strongly, believe me, in the northeast of Scotland. There's going to be a lion roaring tonight, a Scottish lion, and it's going to roar with a voice that no government of whatever political complexion is going to be able to ignore. I think it's going to be a resounding voice, a clear voice, a united voice from Scotland, and I think that is a very good thing.
The former First Minister won his Gordon seat, beating his Liberal Democrat rival Christine Jardine.
Elsewhere Labour has lost one of its safest seats in Scotland, with Sturgeon's party seizing the Kirkcaldy and Cowdenbeath constituency previously held by former Prime Minister Gordon Brown.
The 35 per cent swing in Kirkcaldy is believed to be a new record.
And the SNP also won Edinburgh South West - the seat previously held by former Labour Chancellor and chair of the Better Together campaign during the Scottish independence referendum, Alistair Darling.
Despite the party's stunning surge, the SNP's trouncing of Labour in Scotland may end up costing it greater influence at a national level, as the Conservatives sweep to an unexpected majority government that doesn't require coalition partners.
For the time being, however, the SNP will be celebrating a victory margin so huge that just 10 hours ago Sturgeon laughed off such a result as "unlikely".
That comment came after an exit poll predicted her party would win a total of 58 seats - only two more than the party eventually won.
"I'd treat the exit poll with huge caution. I'm hoping for a good night but I think 58 seats is unlikely! #GE15,' she tweeted.
- Daily Mail