Liverpool midfielder Xabi Alonso was his side's matchwinner but the home side made hard work of their victory over Sunderland at Anfield.
Alonso curled in a 25-yard free-kick but the Reds failed to add to their goal despite dominating the game.
Sunderland had an appeal for handball against Momo Sissoko turned down while Andy Welsh seemed to be unfairly sent off for a shove on Luis Garcia.
Djibril Cisse was Liverpool's main culprit in missing three clear chances.
The match was delayed by 15 minutes because of crowd congestion at Anfield and the signs looked ominous for the Black Cats early on.
Reds skipper Steven Gerrard struck the post with a cross shot after just two minutes while Fernando Morientes headed wide.
A cross-field ball from right-back Steve Finnan was nodded wide by Boudewijn Zenden as Liverpool bossed the game and probed away for an opening.
Cisse, whose Reds future came under the spotlight leading up to the match, spurned a glorious chance when his feint touch from Zenden's cross went agonisingly wide.
Liverpool finally got their breakthrough with Alonso's strike but eased their foot off the pedal to give the visitors hope of an equaliser.
Dean Whitehead beat the offside trap and played a ball across the home six-yard box only to be lacking support with no team-mate on hand for a simple tap-in.
The Black Cats had their appeals for a Sissoko handball waved away following a corner but they gradually began to grow in confidence.
But they reacted angrily shortly after the interval after Cisse blazed over when they thought he should have stopped play with defender Alan Stubbs stricken on the ground.
A Gary Breen error gave Cisse another chance but he disappointingly powered a shot wide before having a goal disallowed for offside.
The Reds could not kill the game off and, while Sunderland were not creating any chances, the 1-0 scoreline always gave them an opportunity of stealing a point.
But the visitors suffered a setback when Welsh was harshly red-carded and went down to a second successive defeat after returning to the top-flight.
Sunderland manager Mick McCarthy:
"It's not a sending off. I spoke to refree Barry Knight and he says he will have a look at it.
"He says Andy swung an arm and that's why he gave it. I don't doubt that will get changed.
"It's sad I'm talking about the referee when we played well, especially in the first half."
Liverpool boss Rafael Benitez:
"Gerrard has a calf problem and some players it seems are tired.
"When we started the game we created three or four chances and you need to score.
"If you are winning 1-0 normally the other team think they can do something. You need to score the second goal."
Liverpool: Reina, Finnan, Hyypia, Carragher, Warnock, Sissoko, Alonso, Gerrard (Luis Garcia 55), Zenden (Riise 63), Morientes, Cisse (Baros 75).
Subs Not Used: Josemi, Carson.
Booked: Gerrard, Sissoko.
Goals: Alonso 24.
Sunderland: Davis, Nosworthy, Breen, Stubbs, Arca, Lawrence (Elliott 66), Miller, Whitehead, Robinson (Woods 81), Welsh, Gray (Brown 66).
Subs Not Used: Caldwell, Joe Murphy.
Sent Off: Welsh (74).
Booked: Breen, Robinson, Nosworthy.
Ref: B Knight (Kent).