It was a battle of the goalkeepers for much of the match, but Illan Meslier put in a striking performance to give his side a chance late on after the Reds failed to convert chance after chance.
The showcase started in dramatic fashion, with Mo Salah coming close to opening the scoring within 40 seconds after miscommunication between Liam Cooper and Meslier.
It didn't shake Leeds too much, though, as they kept their footing in the game and pushed Liverpool high up the pitch.
The Reds had a catastrophic mistake of their own in the third minute - Joe Gomez passed the ball back to where he assumed Alisson was, but the Brazil international was wrong-footed and Rodrigo was presented with an easy tap-in to make it 1-0.
After the opening 10 minutes, in which it seemed not one player would be able to string together a successful sequence of passes, the match began to simmer down ever so slightly.
But in the 13th minute, Mo Salah lit up Anfield by levelling the scoreline, connecting well with a superb cross into the box by Andy Robertson.
Leeds kept themselves in the game, as they continued to press their hosts, but Alisson painted an imposing figure between Liverpool's sticks.
The Reds grew into the match as time went on, but a combination of sloppiness in front of goal and solid defending - at both ends - ensured it remained 1-1 at the break.
Leeds started the second period about as erratic as the first, getting a fair share of the ball but doing very little to inspire with it as Liverpool continued to grow.
For all of their possession - sitting at 67 per cent in the 60th minute - the Reds struggled to carve out threatening goal-scoring opportunities throughout the second-half.
Cooper was once again left red in the face at Anfield, sat down by Salah in the final third just before the 70th minute, but Darwin Nunez was unable to convert the resultant pass one-on-one with Meslier.
The young Frenchman was forced into action again and again before the final whistle, but dealt with every test expertly to keep Leeds in the game.
Liverpool continued to press high into the final minutes, which proved to be costly as Crysencio Summerville pounced on a loose ball to sensationally take all three points at the death with a 2-1 win.
