Connor Wickham sent Sunderland on their way with the opening goal and Cardiff suffered a double blow right on the stroke of half-time when Juan Cala was sent off for conceding a penalty for a foul on Wickham and Fabio Borini scored from the spot.
Substitute Emanuele Giaccherini made the game safe for Sunderland 14 minutes from time when he latched onto Borini's pass to score with one of his first touches after coming off the bench and Wickham completed the rout with is second goal four minutes from the end.
The defeat means Cardiff replace Sunderland at the bottom of the table and two points adrift of safety with only two games remaining.
Sunderland started on the front foot backed by a passionate home crowd and they had early appeats for a penalty waved away when John O'Shea's header appeared to bounce off Kevin Theophile-Catherine's inside the box.
Sebastian Larsson had a sight of goal on eight minutes when he was picked out by Wickham inside the box, but his header at full-stretch was straight at David Marshall.
Cardiff created their first chance of the game on 17 minutes when Colback's headed clearance from Peter Whittingham's corner fell to Don Cowie inside the box, but the midfielder drove his left-footed volley well over the top.
Sunderland made the crucial breakthrough on 26 minutes with the in-form Wickham netted his fourth goal in three games.
Cardiff failed to deal with Larsson's corner and the ball bounced across the six-yard box and Wickham was on hand to brilliantly loop his header into the far corner over Whittingham on the line.
The first half ended in controversy when Cala was sent off for denying Wickham a goalscoring opportunity and Sunderland won a penalty.
Cala gave away the ball and tugged back at Wickham as he tried to race clear on goal and after playing advantage for the foul referee Dowd called the action back and handed Sunderland a spot-kick and defender Cala a straight red card.
Borini took responsibility from the penalty spot and he drilled his shot low into the bottom corner past Marshall.
Sunderland picked up where they left off at the start of the second half and Adam Johnson had appeals for a penalty waved away after he went down in the under a challenge from Kevin Theophile-Catherine.
Jordon Mutch wasted a decent opening for Cardiff just before the hour mark when he got on the end of Whittingham's corner, but he could direct his header wide of the target.
Fabio was lucky to escape a red card after he pushed over Larsson in trying to get the ball back off the Swede to take a quickly-taken free-kick, but the defender only picked up a booking from Dowd.
Vito Mannone was a virtual spectator in the Sunderland goal, but he was called into the action on 65 minutes when he showed great reactions to re-adjust his feet to push away Whittingham's deflected free-kick.
Sunderland made the game safe on 76 minutes when Borini picked out Giacherrini's run with a superb reverse pass and the Italian drilled his shot past the advancing Marshall to send the home fans into raptures.
Sunderland completed Cardiff's miserable day four minutes from time when Wickham netted his second of the day and his fifth goal in three games when he got on the end of Giacherrini's corner to head home past Marshall.