Argentine winger's late strike earns hosts a passage into fourth round after fantastic goal from French winger cancelled out visitors' early opener to deservedly progress
The visitors took the lead in the first half as the Scottish striker bundled the ball home following a corner that forced a save from Tim Krul.
Newcastle were on top for much of the game and deservedly progressed into the fourth round after Ben Arfa's fantastic goal and Jonas Gutierrez's late finish.
The home side began without arguably their two best players of the season as Cheick Tiote and Demba Ba both boarded a plane bound for the African Cup of Nations.
In their place were Mehdi Abeid and Leon Best, respectively, while Gabriel Obertan and Ben Arfa came into the starting line-up after the hosts' 3-0 victory over Manchester United in midweek.
Blackburn took to the field with their form player, Yakubu on the bench. Goodwillie took his place in a 4-5-1 formation with Ruben Rochina in support of the striker.
If the Toon Army were missing their star players, they weren't showing any signs of it in the opening stages, as they forced Blackburn keeper Mark Bunn into three saves in the opening six minutes from Leon Best, Gutierrez and Yohan Cabaye.
Newcastle were, as expected, on top for much of the first half, with Blackburn's only real openings coming via a Morten Gamst Pedersen free-kick that flew off target and the lively Rochina, who had a pot shot that flew wide of Krul's post.
Blackburn manager Steve Kean was not best pleased when Pedersen allowed Danny Simpson to race past him far too easily, and his cross was cleared only as far as Gutierrez, who curled an effort inches wide.
From the resulting goal-kick Bunn was bizarrely booked for time wasting with over an hour of play remaining.
But a corner from Pedersen led to a mix-up in the Newcastle defence, Goodwillie took advantage to prod home the opening goal of the game on the rebound following Grant Hanley's header.
The teams departed at half-time with Blackburn still out in front, leaving Alan Pardew's side with a difficult 45 minutes ahead of them.
Newcastle began on top, controlling the opening 10 minutes of the half, and both sides made early changes, with Mauro Formica coming on for the clearly disappointed Rochina and Shola Ameobi coming on for the ineffectual Obertan, before Newcastle were then forced to replace Simpson with Ryan Taylor.
Just after the hour mark Ameobi had his first chance of the game after Hanley gave the ball away cheaply to Cabaye in the defence, but the striker completely missed the target, skying his effort into the Gallowgate End.
Newcastle were undoubtedly a bigger threat with Ameobi on, however, as they attempted to find an equaliser. Only some fine defending from Steven N'Zonzi prevented the home side's strike pairing of Ameobi and Best grabbing an equaliser.
And just afterwards, Newcastle deservedly levelled the game as Ben Arfa went on a run that beat almost the entire Blackburn defence before slotting through the legs of Bunn, a contender for goal of the season from the winger.
Taylor was beginning to exert himself on the game with some wonderful crossing from the right, and a ball of real quality was met by Mike Williamson, but the defender struck his header against the bar with a little over 10 minutes to play.
Bunn was again called into action minutes later as Cabaye and Gutierrez saw shots saved by the keeper.
It seemed the tie was destined for a replay until Gutierrez found a winner in stoppage time, playing a give-and-go with Best before finishing past Bunn.