Ryan Hardie scored a 53rd minute penalty to send the Pilgrims, who are bottom of the Championship, through to the fifth round.
Their Premier League opposition struggled throughout much of the afternoon and now lost out on another opportunity for silverware.
Liverpool are top of the Premier League, through the Champions League last 16 and the Carabao Cup final against Newcastle in March.
But Sunday's defeat means FA Cup glory is impossible this season and they are therefore unable to win a historic four trophies in manager Arne Slot's debut campaign at Anfield.
The Reds came close to doing so in the 2021/22 season but could only seal victories in the FA Cup and Carabao Cup.
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Liverpool finished one point behind Manchester City in the Premier League and lost against Real Madrid in the Champions League final.
A treble triumph is still on the cards for Arne Slot and his side, but the FA Cup is now out of reach following a shock result at Plymouth.
Speaking on commentary for talkSPORT at a jubilant Home Park, Jim Proudfoot said: "It is the most famous day in Devonian football history, what a victory for Plymouth Argyle!
"There will be no quadruple for Liverpool, top of the Premier League, top of the Champions League, in the League Cup final.
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"But they've been beaten and deservedly so by the side rock-bottom of the Championship, thanks to a nerveless penalty and the most extraordinary save in the ninth minute of stoppage-time.
"Plymouth Argyle, bottom of the Championship, 43 places below Premier League leaders Liverpool.
"Liverpool maybe took liberty with the team selection, Arne Slot picking a side that he believed would be strong enough to come here and win."
Commenting on winners Plymouth again, Proudfoot added: "February 9 2025 is just about the most famous day in their history."
Plymouth are the first side from outside of the Premier League to eliminate the team top of the top-flight since Wigan Athletic against Manchester City in February 2018.
It's also the first time Liverpool have been knocked out of the FA Cup by a lower league opponent while leading the table since January 1984 against Brighton.
Furthermore, Plymouth have reached the fifth round of the FA Cup for the first time since 2006/07 season.
They have already knocked two Premier League clubs out of the competition in the current campaign, with the Brentford the first in the third round.
They had only ever beaten top flight opponents on two occasions in their history beforehand - West Ham in 1961/62 and West Brom in 1983/84.
Plymouth will be ball ten in the FA Cup fifth round draw, which takes place on Monday evening.