Extra-time goals by substitutes Georginio Rutter and Crysencio Summerville and a Ryan Hardie own goal settled the FA Cup fourth-round replay and sealed Leeds’ passage into the last 16 – and a trip to Aston Villa or Chelsea.
Brendan Galloway’s 78th-minute goal for Argyle had cancelled out Wilfried Gnonto’s 66th-minute opener to force extra time with Leeds in the ascendancy for virtually all of the second period.
Farke, whose side welcome Yorkshire rivals Rotherham United in the league this weekend, said: “It was nearly the perfect away performance. We were so dominant, we created so many chances, scored the goals but we also hit the crossbar twice and the post.
“The scoreline flattered us, yes but not that we had to play 120 minutes and it was also a replay.
“I want to say firstly congratulations to Plymouth, a brave side, a confident side, they never know when they are beaten.
“They found a way in both games to get a foot in the door although we were so dominant.
“We dominated the second half, I just saw the statistics that we had 82 per cent of the possession. But Plymouth had the free-kick and they managed to score so they were pretty effective.
“Plymouth scored out of nothing but we showed great heart to win this. We invested so much energy and mentality into the game and showed a real will to win.
“We took risks and pressed them high and also defended with discipline. I am happy with the performance as we gave everything.