Two of Malbranque's treble came from the penalty spot and Mark Fish was also sent off late on to add more misery to the visiting Addicks.
Fulham took the lead in the 59th minute when Luis Boa Morte was allowed to run with the ball in from the left wing and feed Steed Malbranque who finished well.
Malbranque then grabbed his and his club's second on 66 minutes when he notched from the penalty spot after Boa Morte was tripped just inside the box.
Mark Fish then brought down Facundo Sava with three minutes left to play and Malbranque collected his hat-trick with his second penalty.
Fish was also sent off to add insult to injury for Alan Curbishley's side who go crashing out of the cup, while Fulham go into the fifth round.
A penalty also changed the game in Stoke's 3-0 win over Bournemouth at the Britannia Stadium, as Cherries keeper Chris Tardif was sent off on the stroke of half time after bringing down Brynjar Gunnarsson, and Chris Iwelumo scored from the spot for the opener.
Iwelumo grabbed his second against the ten men after 51 minutes and Peter Hoekstra sealed Stoke's progression into the fifth round with the third six minutes before the end.
