The Black Cats put a rocky patch of Championship form behind them to launch another run in the famous competition, having marched all the way to last season's semi-final.
Sunderland bossed the opening 25 minutes, pinning Palace back inside their own half, with Andy Welsh crashing a fifth minute volley against the bar from inside the box on his home debut.
Carl Robinson twice went close, but the game threatened to turn nasty when in-form Eagles striker Andy Johnson clattered Sunderland defender Neil Collins late to earn a booking in the 31st minute.
Collins then had his name taken two minutes later as he went for retribution, chopping Johnson down from behind.
Having made all the running, Sunderland were caught by a sucker punch in the 41st minute as Mikele Leigertwood wriggled free on the right and sent a low cross towards Johnson in the middle. Collins slid in trying to intercept, but could only divert the ball into his own net.
Sunderland refused to buckle and were on level terms in the 44th minute. Michael Hughes was booked for a heavy challenge on Dean Whitehead and Welsh came across to the right to arrow the resulting free-kick into the area.
With forwards and defenders throwing themselves at the ball, it sailed past them all and straight in at the far post for a deserved equaliser.
Mick McCarthy's men made light of the gusty conditions to take up where they left off after the interval and Sunderland were awarded a match-winning penalty on the hour mark.
Fitz Hall bundled Marcus Stewart over in the box and the striker stepped up to take the spot kick, cheekily chipping it straight down the middle as Gabor Kiraly dived to his left.