North East football is officially home to the hope abatement society. As the digital clock on the scoreboard flickered towards 6pm and random epithets were hurled towards the pitch, the Stadium of Light stood largely empty and bereft of energy.

Sunderland had joined Newcastle United and Middlesbrough, their local rivals and brethren in despair, in sapping defeat. They call it a relegation battle, but this feels more like competing shades of surrender.

Having lost 3-0 away to West Bromwich Albion the previous weekend, having spoken of “soul-searching” and “responses”, Sunderland were muted, grim and witless. For all his recent chiding about fitness and mentality, this is the team Roy Keane built; built and deserted.

Nine times it has happened this season; nine times they have lost at home in the Barclays Premier League, nine times their crowd have been sent home with lead in their veins. Sunderland remain four points clear of peril — Hull City, who are seventeenth, play Aston Villa tonight — but their next two games are away before a final-day match at home to Chelsea.

The sense of desperation was unremitting, growing in magnitude as goals from Steven Pienaar and Marouane Fellaini fizzed past Marton Fulop. “We looked fragile and it’s a worry, yes,” Ricky Sbragia, the Sunderland manager, said. “I think the players do care, but there’s a fear, I can’t deny that. We didn’t have a frenzy or a right good go. They could have been more motivated.”

For Everton, winners outside Goodison Park for the first time in the league this year, the circumstances were familiar; spirit vanquished circumstances. “Tony Hibbert and Leon Osman failed fitness tests before the game, Leighton Baines and Lars Jacobsen passed them,” David Moyes said. “We were struggling for a team last night, but they came through and did what we’ve done all season. We just got on with it.”

This was not a day for daintiness. Beauty did not show its face, serenity was absent, pleasure was rationed; instead, there was just a nagging, nauseous fear. As the match ground on, there were chants of “Let’s all laugh at Shearer”, but they were neither deafening nor convincing; home supporters know that for all the travails at Newcastle United, the barbs may yet be returned.

Everton were not particularly fluent, but they have a remorseless quality that guides them through barren patches and they were solid and professional. While neither goalkeeper had a save to make in the opening half — Jô was responsible for the best early chance, accepting a pass from Pienaar before dragging his shot narrowly wide of the right post — the Merseyside team edged towards dominance.

That position, nominal though it had been, was crystallised in the 49th minute with a rare moment of harnessed speed and delicacy. From a throw on the right, Phil Neville threaded the ball to Jô, who, in turn, moved it on to Pienaar. After shooting through Fulop’s legs, the South African wheeled away in delight, completing a reverse somersault in front of his own fans.

Sunderland must also feel as if they have been turned upside down. A campaign that began with heightened expectations and Keane’s ire is close to implosion; they have incurred seven defeats in their past nine matches. “We invested big money and thought we’d have a better return in terms of points on the board by now, but the time to review it is at the end of the season,” Niall Quinn, the chairman, admitted.

Before then, their defending must be addressed with greater urgency. Everton’s second goal was far from glorious and Calum Davenport deserves rebuke for turning his back on Fellaini when menace was apparent. When Pienaar fed possession in from the right, Fellaini was unmarked and unmolested, having time and space to choose his angles. The stadium leaked fans. “I’d have booed myself off today,” Sbragia said.

Sunderland (4-4-2): M Fulop 4 - P Bardsley 4, C Davenport 3, A Ferdinand 3, D Collins 5 - S Malbranque 4, D Whitehead 3, G Leadbitter 5, KRichardson 3 - K Jones 5, D Cissé 3. Substitutes: D Healy 4 (for Cissé, 64min), C Edwards (for Malbranque, 83). Not used: T Tainio, T Ben Haim, D Murphy, P McShane, N Colgan. Next: Bolton Wanderers (a).

Everton (4-4-1-1): T Howard 5 - L Jacobsen 5, J Yobo 7, J Lescott 7, L Baines 6 - D Gosling 6, P Neville 7, T Cahill 6, S Pienaar 8 - M Fellaini 7, Jô 6. Substitutes: J Rodwell (for Jacobsen, 74min), L Saha (for Jô, 81), S Castillo (for Gosling, 87). Not used: C Nash, J Vaughan, K Agard, J Wallace. Next: Tottenham Hotspur (h).

Referee: M Atkinson Attendance: 41,313