Chelsea stay top of the league, three points ahead of rampant Manchester City but anymore low-key performances like this then it won't be long before they are overhauled. By their title rivals.
They may have won 2-0, and other goal, a seventh-minute header from Eden Hazard promised much, but in truth that was as good as it got for much of this dour encounter.
The visitors were reduced to 10 men following the straight red card brandished by Chris Foy on Tom Huddlestone for a brutish lunge on Filipe Luis.
Top-scorer Costa took advantage of the numerical superiority and clipped home the second on 63 minutes.
Chelsea remain three points clear of Manchester City at the top of the pile. City beat Leicester City thanks to a Frank Lampard goal.
The old saying that it's a good sign when a team wins but does not play well could well have being created for this match.
Hull City came to stifle the match, hope for a country-attack and snatch a point or three.
Thankfully for Chelsea fans who did their best to rouse a lethargic Chelsea, they got neither.
Eden Hazard opened the scoring for the Blues after just seven minutes when a simple pass by Nemanja Matic fed Oscar on the left. The Brazil midfielder took just one touch before centering the perfect inward-curling, right-footer that bisected the centre-back pairing of Michael Dawson and Curtis Davies. Up popped Hazard in-between the two to meet the ball and he direct it downwards and out of the grasp of goalkeeper Allan McGregor.
Dawson, for his part was immediately substituted for Alex Bruce, suggesting the former Spurs defender may have been injured in the build -up to the goal.
The visitors' first effort on goal came on 21 minutes when Matic and Mikel were both dispossessed of the ball and it was passed to Sone Alukp. The speed merchant raced on goal, and luckily for the two Chelsea defensive midfielders, shot inches of Petr Cech's crossbar from just inside the Blues' penalty area.
David Meyler was soon in Foy's book for a stupid hand ball in the Chelsea area.
On 31 minutes, Willian raced on from midfield, but after passing Davies, he stupidly decided to hit the deck unchallenged - Foy rightly booked the winger for diving.
The standard of football was poor during the half and after the restart it continued i hype same vein.
There were no changes in personnel at the break for either side.
A snap shot by Jake Livermore minutes after the restart, inched past Cech's right post. In itself not a significant event, but it was the culmination of complete control by the visitors.
Frustration then took hold of the game with a spate of yellow cards.
Gary Cahill can count himself lucky on 53 minutes not to have received a second yellow when he appeared to dive in the Hull City penalty area.
The Hull plays surrounded Foy demanding the card, but the referee simply waved them away.
A solid challenge by Alex Bruce on Willian three minutes later resulted in the boss's son getting a yellow, then incredibly, Diego Costa was added to Foy's book after fallen over from a challenge by Huddlestone.
The former Spurs midfielder then left his studs in a late challenge on Luis, and despite already having a yellow card to his name, was given a straight red card by Foy.
Chelsea could have had a penalty on 63 minutes, and with this referee it would not have been out of character but he adjudged James Chester's handling of the ball in his penalty area after a fine byline cut back to have been accidental.
Steve Bruce then replaced Aluko with Robbie Brady.
Chester was then handed a yellow card after tripping Oscar. This one, at least was a stonewall correct decision by Foy.
With the man advantage, it was no surprise when the Blues increased their lead. While Costa may have clipped the ball past McGregor to notch his 12th league goal of the season on 68 minutes, it was Hazard's mazy run and beautifully executed pass to the Spain striker that was the most eye-catching aspect of the move.
Didier Drogba entered the fray on 78 minutes for midfielder Oscar, with Andre Schurrle close behind for Willian
Quite why Mourinho did not make all three at the same time is beyond me, unless it was to kill off more time, as Ramires was brought on for Mikel with nine minutes left.
Mourinho cut a frustrated figure on the dug out, rarely sitting down.
On Tuesday, Chelsea face Derby County in the quarter-final of the Capital One Cup.
They will need to play much, much better than this to progress into the semi-final.
Teams: Chelsea, Cech, Ivanovic, Cahill, Terry, Luis; Mikel, Matic, Willian, Oscar, Hazard, Costa
Subs, Schwarzer, Zouma, Ramires, Drogba, Schurrle, Remy, Azpilicueta
Hull City, McGregor, Chester, Davies, Meyler, Huddlestone, Livermore, Jelavic, Dawson, aluminium, Robertson, Elmohamady
Subs, Jakupovic, Rosenior, Bruce, Henandez, Brady, Ramirez, Quinn
Referee, Chris Foy