Little over a week after Chelsea, Manchester City, Tottenham and Southampton saw their hopes go up in smoke, Gus Poyet’s side looked like they would follow suit after Hugo Rodallega gave the Championship side a first-half lead.
However, an unfortunate own goal from the otherwise impressive Bettinelli was followed up by a fine strike from Ricardo Alvarez and Jordi Gomez’s penalty as Sunderland secured a 3-1 win at Craven Cottage.
A trip to giant-killing Bradford now awaits in the fifth round for Sunderland, who dominated proceedings.
However, poor finishing and fine goalkeeping from Bettinelli allowed Fulham to make the breakthrough in the 28th minute as Rodallega struck home their first real chance.
Ross McCormack threatened to add to that strike but Sunderland pushed for a leveller which came in slapstick fashion as Bettinelli somehow fumbled a deflected Patrick van Aanholt cross over the line.
It proved the catalyst to a Sunderland comeback and Alvarez, the evening’s standout player, cut in from the right to unleash a fierce drive to put the visitors ahead with 15 minutes remaining.
Gomez’s stoppage-time penalty to a chorus of “cheat, cheat, cheat” rubber-stamped their progress to the fifth round.
Bettinelli, Grimmer, Hutchinson, Bodurov, Stafylidis, Tunnicliffe, Fofana (Christensen 83), Kacaniklic (Roberts 83), McCormack, Woodrow, Rodallega.
Mannone, Reveillere, O’Shea, Vergini, Van Aanholt, Bridcutt, Gomez, Giaccherini (Brown 90), Alvarez (Agnew 87), Fletcher (Graham 74), Defoe.
Paul Tierney (Lancashire).