Liverpool took the honours in the Merseyside derby as Javier Mascherano's deflected first-half shot and Dirk Kuyt's late strike gave them victory at Everton.
The home side dominated for long periods but paid the price for failing to turn possession into goals as Liverpool took full advantage of their rare moments of attacking threat.
Mascherano enjoyed a huge slice of luck as Liverpool opened the scoring after only 12 minutes when his 25-yard shot ricocheted off Joseph Yobo's leg and flew beyond Everton keeper Tim Howard.
And Yobo was at fault when the Reds wrapped up the points with 10 minutes remaining. Steven Gerrard retrieved his sliced penalty area clearance, and when Howard could not hold Albert Riera's powerful effort Kuyt was perfectly placed to turn in the rebound.
In between Everton were left to rue their own carelessness in front of goal and the heroics of Liverpool keeper Pepe Reina as a traumatic week at Goodison Park - with the proposed move to a new stadium in Kirkby rejected by the government - ended with the pain of defeat in the 212th Merseyside derby.
Everton's £10m Russian winger Diniyar Bilyaletdinov scuffed an effort wide from just eight yards with only Reina to beat just after Mascherano's goal.
Jo, playing as Everton's lone front man, twice had the ball in the net as Everton kept Liverpool under constant pressure in the first half, but both goals were rightly ruled out for offside by referee Alan Wiley.
And the crucial moment came when Reina made a stunning double stop after 70 minutes, saving brilliantly from Tim Cahill's header and then recovering instantly to block Marouane Fellaini from the rebound when he looked certain to equalise.
Kuyt then added insult to injury with the second as Liverpool put some gloss on a disappointing week after their Champions League exit.
For all Everton's defiance, they now have only one win in 11 games and face the real prospect of a season of struggle after the riches of fifth place in the Premier League and an FA Cup Final appearance last term.
Rafael Benitez's side were poor for much of a frantic encounter, but victory was the only item on his agenda as he seeks to push Liverpool back into the top four and he will be delighted with the win, no matter how it was achieved.
Everton boss David Moyes produced a surprise in his line-up when Jo got the nod ahead of Louis Saha and Yakubu, who were named on the bench. Saha has been struggling with a calf injury and Yakubu is on his way back from a serious Achilles tendon problem, and their inability to start presented a major problem for Moyes.
And yet Jo emerged as a central figure in an eventful first half dominated by Everton, but one which ended with Liverpool taking the lead.
It came in fortuitous circumstances after 12 minutes, when Mascherano's speculative long-range effort took a crucial touch off Yobo and flew tantalisingly out of the reach of Howard.
Everton responded with real spirit to their ill-fortune and Bilyaletdinov was guilty of a wasting a glorious opportunity to restore equality, sweeping a half-hit effort wide with the goal at his mercy as Liverpool struggled to defend a throw-in.
Jo then thought he had drawn Everton level when he turned home a finish as Everton continued to press, but Fellaini was clearly in an offside position and Goodison Park's celebrations were cut short.
South African Steven Pienaar was comfortably the most composed player on the pitch amid a typically frenetic derby atmosphere, and he was at the heart of all the good things Everton were doing.
But Liverpool almost broke the shackles to double their lead five minutes before the interval when Emiliano Insua arrived on the end of Glen Johnson's cross, but his header brought a fine reflex save from Howard.
Everton had the ball in the net again on the stroke of half-time, again through Jo, but the Brazilian was in an obvious offside position as he stood directly in front of Reina.
Reina had an anxious moment after 57 minutes when he allowed a powerful shot from Pienaar to slip through his grasp, but he was able to recover before the ball slid over the line.
Everton boss Moyes finally introduced Saha for Jo with 25 minutes left in the hope that the striker's undoubted class could overcome his lack of fitness.
Liverpool were unable to pose any sustained attacking threat to Everton, and they were grateful to Reina for a fine double save that kept them on terms with 20 minutes remaining.
Cahill's header from John Heitinga's free-kick looked bound for the bottom corner until Reina dived to his left to save before recovering to block the follow-up effort from Fellaini.
Liverpool made a double change as they attempted to close out what had been an anxious afternoon, sending on Yossi Benayoun and Riera for David Ngog and Fabio Aurelio.
The move reaped rewards as Riera fired in the shot that was too hot for Howard to handle, allowing the lurking Kuyt to pounce from six yards and seal Liverpool's victory.
Riera almost added a third for Liverpool when his shot was saved by Howard - but that would have been cruel on Everton who matched their rivals and more for long spells.