Everton continued their relentless march toward another European qualification as they stretched their unbeaten run to six games with a 2-0 defeat of Hull.
But the Tigers, 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 signalled 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.
Rival managers David Moyes and Phil Brown both had reasons to be upset with
referee Martin Atkinson after Everton's 2-0 win at Goodison Park over a
disappointing Hull side.
Everton boss Moyes was angry with the booking that will mean record signing
Marouane Fellaini is banned for both the upcoming derby battles with Liverpool.
Hull chief Brown, meanwhile, was furious that Everton's first goal by Fellaini
was allowed, despite the Belgian looking in a clear offside position.
He said: "I have heard Tony Pulis (Stoke manager) talking recently about the little clubs not getting the decisions. When I was at Bolton, it was Sam Allardyce's theme and it got to sound like a broken record.
"But our whole season has been unhinged by a succession of officials and decisions we are not happy with. The first goal, with Everton not conceding in the previous five, was always
going to be crucial at Goodison Park.
"But the first was wrong, even though Mikel Arteta's free-kick was a touch of brilliance from a brilliant player. But that would have made it 1-0 at the break and we would still have been in the game.''
He added: "But I have players with blood all over their shirts, so they gave it everything in that second period. But the first goal was a bad decision from an assistant referee who is
looking right along the line of the defence.
"It killed us. We worked on not giving Fellaini space in the six-yard box, and we achieved that. But he was in an offside position in space we had left him in by squeezing out.''
Moyes was delighted with the victory, but angry that he will now lose
He said: "We were in control and Tim Howard had just a couple of catches to make. The downside was the booking for Fellaini. I have seen it now on TV and the Hull lad ducked his head down to about four feet off the ground, Fellaini is looking at the ball and toe-pokes it away.
"It can't seriously be dangerous play, you are entitled to challenge for that. It was a costly decision and clubs do get people suspended. We thought about taking him off at half-time because of the possible problem of him being suspended with another booking. But we were 2-0 up against Newcastle and didn't win, so the most important game is the one we are playing.
"I made the decision, and if we could have got through 15 minutes or so we would have taken him off. But it is another win, another clean sheet and although Hull made it a scrap,
we deserved the win.
"Referees we have had recently have been very good, but I don't think this one was. And we have had an offside goal, that was clear. I will be straight with things that affect both sides, and our first goal was offside. I have to be fair.''