Just before scoring, Mark Wilberforce made a great save from Liverpool's Besian Idrizaj to stop the home side from taking the lead.
Jonathan Howson then forced Willis into a good stop as he nearly made it 2-0.
Leeds almost made it two on the half hour, when Kevin Smith robbed Danny O'Donnell, but he was stopped by Willis who made a another good save with his feet.
Leeds started the second half with Gavin Rothery and Steven McKeown as substitutes and Liverpool with James Smith and Godwin Antwi.
Hammill went close before Antwi also put a header past the post. Kewell came on for Hammill on 63 minutes and could have equalised deep in stoppage time, but completely fluffed a volley.
The Aussie was also on the receiving end of a tackle that saw Walton yellow carded.
Howson then had a superb 30-yarder two minutes before full-time that was tipped away by Willis.
Overall it was a decent display from a young Leeds side and they deserved to come away with the points.
Liverpool: Willis, Raven, Whitbread (Smith h/t), Roque, O'Donnell, Hobbs, Guthrie, Mannix, Calliste, Idrizaj (Antwi h/t), Hammill (Kewell 63).
Leeds: Wilberforce, Madden, Harding (Rothery h/t), Parker, Walton, Marques, Gardner, Bayly, Smith, Howson, Pugh (McKeown h/t, Hird 85).