Everton heaped further pressure on Sunderland manager Peter Reid with a hard fought win at the Stadium of Light.
Kevin Campbell scrambled the ball home in the 28th minute after Tomasz Radzinski had nodded it down from Thomas Gravesen's left-wing centre but the Black Cats paid the penalty for missing several clear cut chances.
Kevin Phillips was the biggest culprit, missing three great opportunities before having a 70th minute penalty kick brilliantly saved by Richard Wright.
Wright was adjudged to have pushed Niall Quinn immediately after the Republic of Ireland international had replaced Jason McAteer, but Wright flung himself to his right to clutch the ball at the second attempt.
Wright denied Phillips in the 70th minute after the England international had met a Michael Gray centre and Phillips could only hit the post from the rebound.
Gavin McCann also wasted a glorious opportunity when left with only Wright to beat and Kevin Kyle blazed wide when sent clear on his first Premiership start.
Campbell's goal lifted Everton and the impressive Gravesen, Mark Pembridge and Li Tie went close to increasing the lead.
Phillips' woe continued early in the second half when he headed an inch-perfect centre from McAteer wide and when Kyle went clear, the Scottish international stumbled over the ball.
The introduction of Quinn lifted Sunderland's hopes but when Phillips squandered the penalty there was little chance of an equaliser as Everton held firm.
Sunderland face an uphill struggle with matches against Leeds United at Elland Road on Wednesday and the visitors Manchester United to the Stadium of Light before next weekend's transfer deadline.
Everton manager David Moyes conceded Sunderland had missed chances to put his side under pressure in the early stages.
"Sunderland should have been goals up in the first 15 minutes," he said. "But they were very unfortunate times but we regrouped and came here to try and win the game.
"Richard Wright was very down after last week's game but he has worked hard in training and they say fortune favours the brave. That was a fantastic penalty save."
Sunderland manager Reid said: "I have a disappointed dressing room of players. They did well, started brightly but could not get a goal. We had the chances but could not fit the ball in the back of the net.
"When Kevin Phillips missed that chance early on I thought it was going to be one of those days and when he missed the penalty, that was it.
"But all credit to Everton they came out strongly and got the goal."