A Gaston Ramirez header was enough to give Middlesbrough only a second win since August and leave Hull stuck in the Premier League relegation zone.
Ramirez, the game's outstanding player, nodded in Viktor Fischer's corner after being left unmarked at the back post.
Fischer earlier had a goal ruled out for offside, while Boro striker Alvaro Negredo wasted two good chances.
Hull, who have lost eight of their past 10 league games, barely made it out of their own half.
The Tigers remain 19th in the table, two points above bottom club Swansea and one from safety.