Plymouth faced a Brentford side that started without Bryan Mbeumo and Yoane Wissa, who have scored 23 league goals between them.
But their starting line-up included Denmark international Mikkel Damsgaard, who has bagged seven assists this season, as well as other regulars like Sepp van den Berg, Kevin Schade and Mads Roerslev.
Plymouth, though, went toe-to-toe with them and hardly gave the hosts an inch, after overcoming early blushes when they allowed Fabio Carvalho to have a couple of sighters at their goal.
“The plan this week was to be organised, to be in our shape, to come to a Premier League team and make it as difficult as we could for them and to have a bit of quality on the ball,” said interim coach Nancekivell after the game.
And his players executed that plan to perfection as they remained solid even after Thomas Frank introduced Mbeumo, Wissa and Keane Lewis-Potter off the bench – before Whittaker produced the moment of magic.
The 24-year-old, who scored 20 goals last season, cut in from the right and – with the Brentford defence applying little pressure – planted a low drive into the bottom corner to the delight of the away end.
“If we continue performances like that there’s no reason why we can’t accomplish staying in the league,” said Nancekivell, who will be part of Muslic’s backroom staff.
“I am proud of everybody, and I’m pleased for the supporters. It’s a big day for us. The FA Cup brings that romance and we’ve put a little bit of history in it by getting the win.”