Hull grabbed their winner in fortuitous circumstances, as Liam Rosenior curled a cross in from the right and, before Yannick Sagbo could connect with it, Cuellar nodded past his own goalkeeper 25 minutes in.
The match slipped even further from the visitors' grasp at the end of the first half when Lee Cattermole was shown his seventh Premier League red card for a wild tackle on Ahmed El Mohamady.
And after Andrea Dossena had followed him down the tunnel two minutes later after stamping on David Meyler's shin, Hull predictably dominated the second half.
Chances were more apparent in the final 15 minutes, as Steven Fletcher was denied by Steve Harper, before Jake Livermore hit the post, but Hull had already done enough to claim a win that extended their unbeaten run at home in the Premier League to five matches.
Steve Bruce made just the one change from the Hull side that lost to Tottenham in their last Premier League encounter, as Livermore returned.
Fabio Borini’s late winning goal in the north-east derby with Newcastle earned the Italian his second league start of the season for Sunderland, as he replaced Adam Johnson in their only alteration.
Goalscoring opportunities were few and far between early on, but the hosts almost took a 17th-minute lead when Livermore flicked Tom Huddlestone’s left-wing free-kick just past the far post.
Their next chance did find the net, however, as Rosenior’s controlled cross from the right was headed past his goalkeeper Keiren Westwood by Cuellar.
A collision with Paul McShane then forced Westwood off and his replacement, Vito Mannone, almost conceded just a few moments after coming on, but Phil Bardsley deflected Sagbo’s low shot wide.
First-half stoppage time saw Sunderland’s task become an almost impossible one as Cattermole received a straight red card, and Dossena soon followed him for a crude stamp on Meyler.
Manager Gus Poyet reacted to the red cards by introducing Johnson and Wes Brown, with the latter making his first league appearance since January 2012.
Hull looked to make the most of their numerical advantage as quickly as possible, but George Boyd’s left-footed effort in the 53rd minute flew narrowly wide of the target.
Mannone's goal was coming under increased pressure by the hour mark, and the Italian did well to deny Livermore as the on-loan Spurs midfielder shot from distance.
Both sides created chances in the final 15 minutes as Fletcher fired straight at Harper when one-on-one, while Livermore struck the post with a long-range effort, but Hull held on for slender victory.
