Salif Diao sent Liverpool to the top of the Barclaycard Premiership with a neat finish from compatriot El Hadji Diouf's centre, at Elland Road this afternoon.
The Senegal midfielder nipped in ahead of Paul Robinson and Jonathan Woodgate to clip the ball calmly into the net at the near post.
The points could easily have been shared, however, had Harry Kewell netted a sitter in the 87th minute.
Kewell latched onto the end of Mark Viduka's cross after the big striker pounced on a John Arne Riise error that had caught out captain Sami Hyypia.
After neatly dummying Diao and Carragher, Kewell was confronted by the onrushing Jerzy Dudek. The Australian shifted it onto his right foot but couldn't keep it down.
Liverpool started the brighter of the two sides and for the first 25 minutes looked lively despite not testing keeper Paul Robinson.
Leeds got back into the swing of things after Terry Venables shifted the midfield from a diamond formation back to a flat four. They could well have led at half-time; Kewell forced Dudek into an athletic save and was later denied by the crossbar.
Sandwiched between Kewell's efforts was a rasping shot from Alan Smith that had Elland Road on its feet as it crept agonisingly wide of the right hand post.
A bit of an edge crept into the game late in the half as Lee Bowyer inexplicably charged Bruno Cheyrou into the advertising hoardings.
A heated exchange then developed on the touchline while Smith received treatment. It lead to strong words from fourth official Jeff Winter as the 21-year-old bemoaned his fate.
Venables stepped out of the dugout to have his say. Coach Brian Kidd then followed but needed to be restrained by his manager as the argument continued.
Smith received four stitches in his knee at half time and was replaced soon into the second half by Mark Viduka.
The change seemed to narrow the homeside up a bit and they hadn't the chances that the latter stages of the first half had preempted.
Ultimately, Liverpool - as they have done so well in the past - kept the Leeds chances to a minimum and struck their goal with clinical efficiency. They defended with discipline to take all three points and condemn Leeds to their third home defeat of the campaign.
