Everton continued their relentless march toward another European qualification as they stretched their unbeaten run to six games, all without conceding a goal.
But Hull, after such a fine start to their first season in the top flight, have now won just one league game in 11 and must be thankful for those early points.
After Marouane Fellaini's opening early header--later followed by his 10th booking of the season--Hull were rarely in it. The game was virtually over when Mikel Arteta lashed home a fine free-kick in first-half injury time.
But it was a bitter-sweet day for Everton, who will now be without the suspended Fellaini for their two forthcoming derby matches with Liverpool.
Everton made one change from the side that won at Macclesfield last week in the FA Cup, midfielder Fellaini returning in place of striker Victor Anichebe.
Hull, who had not played at Goodison Park since 1964, rested several players in their Cup draw at Newcastle last weekend, but Boaz Myhill, Ian Ashbee, Nick Barmby, Bernard Mendy, Marlon King and Kamil Zayatte all returned for this one.
Barmby, who left Goodison for Liverpool almost nine years ago, suffered some mild abuse from the home fans who have long memories about such acts.
But it did not bother the now veteran midfielder who was very much part of Hull's bright start.
Phil Brown's side were competitive, quick into the tackle, and could have scored after 11 minutes when Michael Turner rose unchallenged to head just over from a corner.
But it was Everton who were soon in front. Leighton Baines fired over an 18th-minute cross, and Fellaini was poorly marked in the six-yard box when he guided a header into the far corner.
Nine minutes later Fellaini should have had a second. But his header from six yards out following Tim Cahill's cross from the right, went wide of a post.
Referee Martin Atkinson had let quite a lot go unpunished in an increasingly fractious match, but he had the book out to caution Mendy for a foul on Baines.
This was a mark of Everton's increased possession, as they pushed Hull back. But despite Steven Pienaar and Baines frequently getting to the byline, the final ball into the box was not good enough.
But when Turner fouled Cahill some 30 yards out in first-half injury time, there was nothing wrong with Arteta's stunning delivery from the free-kick. His curling effort crashed past Myhill's flaying right-hand for Everton's second.
Six minutes into the second-half, Everton's joy at a two-goal lead was tainted by the 10th booking of the season for Fellaini, which now rules him out of the next two matches--the derbies with Liverpool.
The Belgian had fouled Turner, and referee Atkinson pointedly signaled several fouls committed by the midfielder around the pitch earlier.
Hull had Sam Ricketts and Zayatte booked as the game became heated with Cahill also receiving a yellow card.
Hull also sent on Craig Fagan and Daniel Cousin for Dean Marney and Geovanni.
Everton then sent on Victor Anichebe for Cahill, and Hull replaced Paul McShane with Peter Halmosi, Cousin being booked for a foul on Phil Jagielka.
But by now the game had deteriorated into a niggly affair, with barely any goal mouth action as Everton hung on to their lead with Hull failing to get within range of Tim Howard.
That is until injury-time when Ashbee blasted just over from outside the box. Teenager Jack Rodwell, who is expected to sign a new long-term contract next week, replaced Arteta in the final seconds.
There was still time for Fagan to be booked for a late foul on Fellaini.
