The Pilgrims claimed one of the shocks of the weekend when they beat Premier League outfit Brentford 1-0 away from home.
Liverpool, who beat Accrington Stanley 4-0, will travel to Home Park whilst holders Manchester United are at home to Leicester.
Ruben Amorim's side sealed a dramatic penalty shootout win over Arsenal despite being down to ten men.
Amorim will face his predecessor Ruud van Nistelrooy, who was in interim charge at United before moving to Leicester permanently.
Chelsea will travel to Brighton, with the winner of Leyton Orient vs Derby playing at home against Manchester City.
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Tottenham were taken to extra-time by Tamworth but won 3-0 to earn a trip to Aston Villa.
Frank Lampard's Coventry City will welcome Ipswich Town, who were comfortable winners over Bristol Rovers.
Newcastle came from behind at home to beat Bromley 3-1, with Eddie Howe's side now set to face Birmingham City at St Andrew's.
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Alongside this fixture, three other ties will be decided during the week following postponements this weekend due to the weather.
Leyton Orient vs Derby, Mansfield Town vs Wigan Athletic and Preston North End vs Charlton all await victors.
Like the third round, there will be no VAR in use in the FA Cup fourth round and there will continue to be no replays.
Fourth round fixtures will take place across the weekend of February 8.
Man United boss Amorim is relishing a meeting with club legend and now-Leicester manager Van Nistelrooy in the next round.
He said: "First of all, I'm going to meet, for the first time, Ruud van Nistelrooy.
"I want to give him a hug! I will call him, he's a class guy. But we want to win, to pass to the next round.
"The FA Cup is a very good competition, I really enjoy it.
"I talked with Ruud before I came. I'm looking forward to speaking with him.
"Maybe we'll be divided because he loves this club but we need to win.