David Ngog struck the only goal as a much-changed Liverpool side sneaked past a fired-up Leeds in the Carling Cup.
The Premier League giants were outplayed by the League One leaders for much of the third-round tie but Ngog netted against the run of play after 65 minutes.
Leeds spurned a number of chances as Elland Road enjoyed a big-game atmosphere once again, but a lack of composure in front of goal cost them.
Leeds striker Jermaine Beckford endured a particularly frustrating night as he missed several good chances and had a goal in the first half disallowed, a decision that enraged the home side’s fans in a crowd of 38,168.
Jamie Carragher, who took over the captaincy, and Javier Mascherano were the only survivors from the Reds side which won at West Ham last weekend.
Leeds were keen to attack and gave warning when Snodgrass broke free, although his cross was easily claimed by Liverpool keeper Diego Cavalieri.
Ngog, starting up front alone, then got into the game with a couple of breaks but saw a long-range shot after a neat turn blocked.
Michael Doyle then squandered a glorious chance for Leeds but from Snodgrass’s perfect cross he headed wide from eight yards with the goal at his mercy.
The Yorkshire side had the ball in the net after 11 minutes when Beckford turned in Michalik's goalbound header from close range but Wiley ruled the striker offside.
Albert Riera should have given Liverpool the lead, against the run of play, on the stroke of half-time after meeting a Fabio Aurelio free-kick but Higgs saved his firm header.
Leeds continued to look the most likely side in the second half and Beckford raced on to a long bouncing ball but scuffed his shot when any firm contact might have beaten Cavalieri.
The Leeds striker had another gilt-edged opportunity when Bradley Johnson crossed from the byline after 63 minutes but, after turning brilliantly, he sent his shot over.
Leeds paid the price as Liverpool went ahead two minutes later.
Mascherano mis-hit a shot from the edge of the area but Ngog reacted quickly and seized on the ball to tuck past Higgs.
Liverpool brought on Glen Johnson and Steven Gerrard in an attempt to see out the game and Gerrard almost made doubly sure of victory as time ran down but fired into the side-netting and then straight at Cavalieri.