Sitting only three points behind Arsenal and Manchester United, who are level in fourth on 38 points, the Blues kept their sixth consecutive clean sheet in a tough match which saw seven yellow cards.
Two first-half goals from Marouane Fellaini and Mikel Arteta sealed the points as Hull failed to put any pressure on the blue back four.
The home side started the brighter of the two, with both wing-backs, Leighton Baines and Tony Hibbert, getting forward, but with the visitors almost playing five at the back with captain Ian Ashbee just in front of the defence, the Blues failed to connect with the string of balls played into the box.
Hull were making their presence felt with a number of strong challenges and it was a battling Marlon King that won his side a corner to create the first real chance of the game, but an unmarked Michael Turner could only power his header over the bar.
Everton looked dangerous with the ball at their feet and the breakthrough came in the 18th minute when a neat one-two between Baines and Steven Pienaar saw the left-back whip in a near-post cross onto the head of Marouane Fellaini, who did well to glance it inside the far post.
Despite replays showing the tall midfielder standing a yard offside the flag stayed down and the home side had a deserved lead.
The Blues kept the ball well, forcing Hull to sit deep inside their own half and the lead could have been doubled on 25 minutes when Leon Osman jinked his way past two players on the Hull touchline and fizz the ball across the front of goal but no one could manage a final touch.
With still no fit first-team strikers Tim Cahill was once again playing the role as lone frontman, supported closely by Fellaini and it was that pair who linked up moments later when a cross from the Australian found the goal-scorer leaping highest in the box, but his effort failed to test Boaz Myhill.
Everton started turning the screw, throwing wave after wave of attack at the visitors but the central defensive pairing of Turner and Kamil Zayatte seemed to be standing strong until a needless shove in the back by Turner on Cahill gifted the Toffees a free-kick just before the break.
Making his 150th appearance for his club, Arteta stepped up to blast a 25-yarder through the wall and into the top corner, leaving Myhill with no chance and taking his side in at the break two goals to the good.
The second half didn't start well for Fellaini who was harshly yellow-carded for what was adjudged to be a high boot and a string of little fouls accumulated from the first half.
The 47th minute booking left a sour taste in the young Belgian's mouth as it was his tenth of the season giving him an automatic two-match ban meaning he will miss the league and cup derbies against Liverpool.
Everton felt they should have extended the lead when Cahill out-jumped Turner on the halfway line sending, Osman running with the ball in a three-on-one attack.
Despite Pienaar and Fellaini offering their support the winger failed to release the ball early, giving Hull the chance to get a foot in and clear the ball.
Having struggled for possession during the whole game, Phil Brown's side never looked like troubling Tim Howard's goal and the home side felt they should have put the game out of reach when substitute Victor Anichebe was felled just inside the box.
But after referee Martin Atkinson waived play on, the ball dropped kindly to Osman on the penalty spot, but his effort flew high over the bar.