Having bowed out of the FA Cup and UEFA Champions League in the past seven days, Man City's Premier League title hopes were in danger of suffering a dent when Kompany was given his marching orders after just 10 minutes.
However, David Silva netted a wonderful goal three minutes later and Manuel Pellegrini's side held firm in a commanding performance.
Edin Dzeko added a late second to seal three vital points as City climbed back into second place and kept the pressure on Chelsea at the top.
Pellegrini made four changes to his line-up following the midweek defeat in Barcelona, but was quickly forced to rethink his strategy after Kompany was dismissed inside the opening 10 minutes.
Nikica Jelavic had already threatened a couple of times in the early stages when he challenged Kompany for the ball 25 yards from goal and was hauled down by the Belgian centre-back.
Referee Lee Mason had no hesitation in brandishing a straight red card even though Kompany, protesting that the initial foul had been from Jelavic, appeared hugely frustrated as he trudged off and kicked the wall on his way through the tunnel.
Man City responded to the setback in perfect fashion, though, as Silva produced a moment of magic out of nowhere to break the deadlock on 13 minutes. There did not look to be any imminent danger as the Spaniard picked up a short pass from Yaya Toure, but he was able to curl a sublime strike from distance beyond the reach of Allan McGregor and into the top corner.
With a lead to protect, Man City were content to sit back as Javi Garcia dropped back alongside Martin Demichelis in defence, allowing Hull more of the ball in midfield.
However, the visiting side remained a threat on the counter-attack and nearly doubled their lead on the half-hour mark when Pablo Zabaleta struck the crossbar with a thunderous volley from the edge of the area.
Hull found it difficult to carve out chances and started losing their patience, with Ahmed Elmohamady perhaps fortunate to only receive a yellow card for a wild tackle on Silva.
David Meyler, on the wrong end of an Alan Pardew headbutt in Hull's previous league game, briefly thought he had equalised with a ferocious strike from 12 yards, but the flag was correctly raised for offside.
Jake Livermore shot powerfully wide from long range just before the interval, and Hull began to build more momentum as the second half began after bringing on Sone Aluko for Maynor Figueroa.
Joe Hart was finally called into action to save from Shane Long, but the Tigers' attacks were repeatedly cut short by offside calls as the much-maligned Demichelis marshalled his defence impressively.
Hull did manage to work their way into a good position in the 69th minute, but George Boyd went down in the area after playing the ball round Hart. Replays showed there was no contact and as referee Mason waved away appeals for a penalty, a furious Hart confronted Boyd for diving, landing the England keeper a booking as the Hull midfielder escaped without punishment.
Boyd was involved again moments later when he was barged by Fernandinho in an aerial challenge but again Mason let play go on, and Man City should have put the result beyond doubt within minutes.
The ball broke kindly for Fernandinho in the Hull box after a great piece of skill by the sparkling Silva, but he squandered a glorious opportunity to make it 2-0 as he shot horribly wide from the centre of the area.
Dzeko was also denied by a fine McGregor save as Man City launched a late break, but he was able to grab his goal in the 90th minute with a neat finish after being played through by Silva's sumptuous outside-of-the-boot pass.