Vincent Kompany was sent off in the early stages, but the visitors earned the win to close within six points of first-place Chelsea.
Captain Kompany saw red in the opening 10 minutes Saturday after hauling down Nikica Jelavic as the striker looked set to race through on goal, but David Silva's superb curling effort handed the visitors the lead just four minutes later.
Pablo Zabaleta hit the crossbar before the break as Manuel Pellegrini's reorganized charges continued to underline their attacking prowess, but the hosts also had their moments. Jelavic, restored to the starting lineup along with Shane Long after Hull's FA Cup exploits, was frequently a threat and David Meyler had an effort ruled out for offside.
Hull upped the pressure after the interval but was undone by Edin Dzeko's late goal, assisted by Silva, as its search for a home league win in 2014 continues.
Pellegrini may have seen his dreams of a historic quadruple go up in smoke this month, with his side's FA Cup and UEFA Champions League campaigns brought to an end in the space of four days, but the top-flight crown remains within his reach.
Steve Bruce's side remains uncomfortably close to the bottom three, but the game appeared to swing in the hosts' favor when Kompany resorted to bringing Jelavic down following a physical tussle 30 yards from goal.
Referee Lee Mason opted to send the Belgian off despite his protest that he had been fouled first, with Kompany kicking out at a wall as he stormed down the tunnel.
But Silva turned Manchester City's frustration into joy when he seized on the opportunity to shoot from 25 yards and produced a glorious effort that swerved inside Allan McGregor's right-hand post, ending his 17-game goal drought.
The goal buoyed Pellegrini's men but they still had defending to do when Long's searching right-wing cross almost found Jelavic, with Martin Demichelis doing just enough to snuff out the danger.
Zabaleta struck the underside of the crossbar with a dipping volley at the other end on the half-hour mark, the ball bouncing on the line and out to safety.
Meyler saw an effort ruled out for an offside in the buildup and Jake Livermore flashed a low, skidding effort narrowly wide of Joe Hart's upright on the stroke of halftime as Hull sent a timely reminder that it was still very much in the contest.
Jelavic was again involved early in the second half, making poor contact with halftime substitute Sone Aluko's dangerous free kick to leave Hart with a simple save.
George Boyd, on for Meyler just before the hour, took a tumble in the box with Hart nearby but Mason awarded a goal kick and booked the goalkeeper for his part in a confrontation that followed.
Dzeko put the game to bed in stoppage time after wasting an earlier effort as the visitors went some way to avenge defeat on their last trip to the KC Stadium and put the bitter disappointment of Champions League elimination behind them.