And . . . relax. Well, that is what it looked like: a collective exhalation from Sunderland’s players now that Ricky Sbragia has been named as permanent manager after his stint as caretaker. Roy Keane’s departure was the cue for a release of tension that inspired expressive wins over West Bromwich Albion and Hull City, but this was altogether too mellow. Everton were not just superior, they were supreme.

Tim Howard, the home side’s goalkeeper, had to make only one save all match – and that was from a modest long-distance effort by Carlos Edwards. Even allowing for the home side’s greater prowess, Sunderland’s performance was entirely bland and featureless, possessing neither vibrancy nor thirst.

The players had agitated for Sbragia’s appointment, but it is a curious truth that teams often respond better to insecurity than to authority. An uncertain future can provoke impressive results, but when doubt is removed over a managerial vacancy, other doubts can creep in.

Sbragia’s record stands at two wins and a draw in five games. He may prove strong and flexible enough to make a successful transition from being Keane’s follower into Sunderland’s leader, but Saturday’s appointment of a man with no prior managerial experience is a mild surprise considering the struggles this season of two top-flight greenhorns, Tony Adams and Paul Ince – and of two former assistants last term, Sammy Lee at Bolton Wanderers and Chris Hutchings at Wigan Athletic.

While Sbragia must mop up after Keane’s transfer excesses and down-size a squad of 50-odd, David Moyes has the opposite challenge. As in the Boxing Day win over Middlesbrough, injuries forced Everton to operate without a conventional striker.

“Wingless Wonders” did just fine for Alf Ramsey and Moyes is also profiting from the versatility of his midfield players. Tim Cahill – who has scored more goals this term than Emile Heskey, incidentally – and Marouane Fellaini were the nominal front two, both strong in the air and making their typical rumbustious runs a few yards farther up the pitch than normal. The formation was a sort of 4-4-2 cum 4-6-0.

The Strikerless Sensations? “No one in the camp’s made anything of the striker problem,” Steve Round, the Everton assistant manager, said. “We’ve got goals all over the team. We’re quite comfortable with what we’ve got. We were exceptional, especially in the second half when we controlled the game.”

Anyway, who needs strikers when you can score from set-pieces? Mikel Arteta, a source of such invention that some of his passes should be registered at the Patent Office, was the match-winner. After ten minutes he drilled a dipping, deviating free kick that whistled over the wall and was too much for Marton Fulop to handle in the Sunderland goal.

Seventeen minutes later, another free kick from the Basque rebounded off the wall, he tried again on the volley and it was deflected past Fulop by Teemu Tainio. Cahill should have added a third, again from Arteta’s set-piece, but he headed a simple chance narrowly wide. With Everton confident and composed and Sunderland’s midfield operating on standby mode, two goals were more than enough.

Sbragia must have been grateful that the result did not come close to the 7-1 mauling Sunderland suffered at Goodison Park last season in his first match as the club’s coach, but a deserved shine was added to the score-line late on when Dan Gosling, the 18-year-old signed from Plymouth Argyle in January and making his second Everton appearance, tapped in Joleon Lescott's low left-wing cross from six yards.

It was Everton’s fourth successive clean sheet and a victory that begins to correct a curious imbalance. Before yesterday’s game, they had won only once at home in the Barclays Premier League but seven times on the road. “The top six has always been the target,” Round said. “And if you’re in the top six, can you get to the Champions League? We haven’t got the finances to compete with some other teams, but we will try and get there on organisation and spirit.”

Is it really possible to beat Liverpool, Arsenal and Manchester United – three of Everton’s next four opponents in the league – without a recognised striker? If Moyes’s injury problems ease or he signs a forward next month, we may never know. But while it lasts, it is an intriguing experiment.

Everton (4-4-2): T Howard 6 A Hibbert 6 P Jagielka 7 J Lescott 7 L Baines 6 L Osman 6 P Neville 7 M Arteta 8 S Pienaar 7 M Fellaini 7 T Cahill 6 Substitutes D Gosling 6 (for Osman, 70min), V Anichebe (for Fellaini, 77), L Jutkiewicz (for Cahill, 85). Not used C Nash, A van der Meyde, J Rodwell, J P Kissock. Next: Hull City (h)

Sunderland (4-4-2): M Fulop 5 P Bardsley 5 N Nosworthy 6 D Collins 5 K Richardson 6 S Malbranque 4 D Whitehead 5 T Tainio 5 D Murphy 5 D Cissé 5 K Jones 5 Substitutes C Edwards 5 (for Malbranque, 46), D Yorke (for Tainio, 75), D Healy (for Cissé, 75). Not used J Colback, J Henderson, R Prica, N Colgan. Next: Middlesbrough (a)

Referee R Styles Attendance 39,146