| Tim Cahill broke the deadlock for Everton in the 34th minute [GALLO/GETTY]
Liverpool have rid themselves of unpopular owners but not their relegation form as local rivals Everton inflicted a 2-0 loss on the side in front of new owner John W Henry.
In Sunday's other Premiership game, Manchester City climbed to second, two points behind Chelsea, after Carlos Tevez's double helped to secure a 3-2 victory over battling Blackpool.
At Goodison Park, goals from Tim Cahill and Mikel Arteta either side of the break left Liverpool off the bottom of the table only on goal difference after eight matches.
Liverpool looked devoid of guile and attacking threat, quickly banishing hopes that ousting Tom Hicks and George Gillett Jr in favour of the owners of baseball's Boston Red Sox would solve their troubles.
Pressure on Liverpool
While Liverpool's legal team won a week of court battles to allow New England Sports Venture (NESV) to oust the previous regime, the players could not replicate their success on the pitch.
Henry and Tom Werner, the chairman of NESV, saw the side they had purchased for $480m on Friday contained inside its own half from the outset as Everton confidently piled on the pressure.
The home side squandered the best of its early chances when Phil Jagielka shot over after Arteta's free kick came off the wall.
But managing his first Merseyside derby was becoming an uncomfortable experience for Roy Hodgson as he berated sloppy Liverpool play from the sidelines.
Werner had earlier said that Hodgson's job was safe under the new regime.
It took almost 25 minutes for Liverpool to get sight of goal, with struggling striker Fernando Torres flicking in a header that was turned over by US goalkeeper Tim Howard.
Henry had his head in his hands and the joy from completing the takeover on Friday was fast diminishing when in the 34th minute Cahill broke the deadlock.
Pepe Reina's low diving save had thwarted a Yakubu Ayegbeni shot, but he could not stop Cahill from lashing the ball inside the near post.
Seamus Coleman did all the hard work, forcing his way down the left flank to the byline and then cutting the ball back for Cahill.
Liverpool were unable to penetrate Everton and the deficit was doubled after the break when Arteta picked up Leighton Baines' corner on the edge of the penalty area and unleashed a fierce volley past Reina.
While it did rouse Liverpool into a more assertive approach, their attacks fizzled out.
Torres lashed over after latching onto Maxi Rodriguez's throughball, with the Spain striker looking a shadow of the player who netted 34 goals in 2007-08.
Liverpool remain in the bottom three with just one win this season, while Everton move up to 11th.
At Bloomfield Road, City took full advantage after defending champions Chelsea had being held 0-0 by Aston Villa on Saturday.
Tevez chipped home David Silva's low cross to put City ahead in the 67th minute and the Argentina striker sent a deflected drive into the net 11 minutes later - soon after Marlon Harewood had headed Blackpool level.
Silva looked to have settled the match when he curled in his first league goal in the 90th, but Gary Taylor-Fletcher still found time to pull one back for Blackpool.
"They put us under a lot pressure, which we knew they would," City winger James Milner said.
"We managed to ride the storm, score three good goals, and hung on at the end. The best is to come but it's the sign of a good team when they can win and not play the best football.
"Hopefully we can keep improving as a team, keep moving forward and hopefully you'll see the best of us soon."
Tevez's brace took his tally to 28 goals in his last 31 league games.
"He's carried on from last season," City midfielder Gareth Barry said. "He's a world class striker."
City are three points ahead of Arsenal, Manchester United and Tottenham, while Blackpool remain 10th with 10 points in their first season in the top flight since 1971.