Graham Carey was the hero as Plymouth booked a third-round date with Liverpool after beating Newport 1-0 in their FA Cup second round replay.
The striker's 113th minute penalty was enough to decide a tight game, which looked to be heading for a shoot-out.
Argyle's Paul Garita had earlier missed a 97th minute spot-kick but Carey made no mistake in the second half of extra-time, after the two teams could not be split following 180 minutes of football.
It was a cagey 90 minutes from the off, as both sides saw chances go begging, with Carey going close with a free-kick in the first half.
Plymouth goalkeeper Luke McCormick made a series of stops to deny Josh O'Hanlon and Rhys Healey, while Joe Day denied Carey in the 86th minute.
But the drama came late when Garita's penalty cannoned back off the post in extra-time following Jennison Myrie-Williams' handball while, at the other end, McCormack was on hand again to smartly deny Healey.
Carey then made amends, tucking away his late penalty after Darren Jones had fouled David Goodwillie, to book the Pilgrims' date against the seven-time cup winners.
The third-round fixture on January 8 at Anfield is expected to be worth around £500,000 in broadcast fees and ticket revenue.