Scott Sinclair's superb late strike set the seal on Plymouth's victory over valiant League Two side Barnet.
Plymouth's Barry Hayles tries to close down Jason Puncheon
The first half ended goalless with Barnet's hard-working team restricting Argyle to long-range efforts.
Adam Birchall went close for Barnet after the break, but Hasney Aljofree put Plymouth ahead from the spot after Joe Devera's foul on David Norris.
And Sinclair made sure of the result as he beat two players before slotting home with seven minutes left.
Barnet were not wanting for effort at Underhill, but lacked the composure at key times to repeat the third-round win over Colchester.
Argyle midfielder Lilian Nalis had a pot shot from 35 yards early on, but failed to trouble Barnet keeper Ross Flitney.
Andy Hessenthaler - at 41, the oldest outfield player in the Football League - continued to impress in midfield for Barnet, making several important tackles.
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But genuine goalscoring opportunities were hard to come by, with Barry Hayles' well-hit effort ending up over the bar.
Plymouth's Akos Buzsaky sent in a dangerous free-kick shortly before the break, but Flitney saved well to keep the scores level.
Barnet enjoyed plenty of possession in the second half but lacked the guile to carve out any decent chances.
Argyle keeper Luke McCormick did have to be alert to keep out Birchall's drive but had little else to do.
Argyle made the breakthrough on 67 minutes when Devera fouled Norris in the area, and Aljofree made no mistake with a cool effort.
Soon after, Norris created some space for himself but his drive was parried by Flitney before Ismail Yakubu cleared Barnet's lines.
But the best moment of the match came when Sinclair, on-loan at Argyle from Premiership champions Chelsea, burst past two defenders before slotting the ball past Flitney.
Plymouth manager Ian Holloway:
"Scott, who's on loan from Chelsea, is a great talent and his goal was superb.
"We're just going to hope Chelsea boss Jose Mourinho doesn't watch it on TV because we want to keep him for a bit longer.
"They are going to want to take him back and I'd be an idiot if I thought that I'd be able to hold on to him."
Barnet boss Paul Fairclough:
"I thought we gave them a real run for their money.
"We outplayed them but the penalty shattered our confidence and some of the lads let their heads drop.
"Some pundits wrote us off before the game. If they had come today they'd have seen our team outplaying a side a way above us in the league."
Barnet: Flitney, Devera (Allen 89), Yakubu, King, Nicolau, Cogan (Hatch 71), Bailey, Hessenthaler, Graham, Puncheon, Birchall.
Subs Not Used: Jaimez-Ruiz, Warhurst, Charles.
Booked: Devera, Bailey.
Plymouth: McCormick, Connolly, Aljofree, Seip, Capaldi, Norris, Buzsaky (Summerfield 64), Nalis, Halmosi (Sinclair 60), Hayles, Gallen.
Subs Not Used: Hodges, Timar, Gosling.
Booked: Aljofree, Capaldi.
Goals: Aljofree 67 pen, Sinclair 83.
Ref: P Walton (Northamptonshire).