Van der Vaart came closest for the home side in the first half, turning inside the penalty area but Dudek saved well.
Liverpool's best chance fell to Diouf on 57 minutes but his tame shot across goal was deflected by the keeper and went on to hit the corner flag.
Wonderful football from substitute Jari Litmanen gave Van der Vaart another chance to break the deadlock on 70 minutes but his shot from outside the area cleared the bar.
Hyypia almost put the ball into his own net on 80 minutes but it came off the outside of the post for an Ajax corner.
Dudek got a hand to the ball and pushed it onto the bar in a goalmouth scramble in the last two minutes of the game then saved well from Litmanen in the final few seconds to prevent defeat.
Gerard Houllier's side now face Galatasaray at 5.00pm on Sunday, while Ajax take on Inter Milan later the same night.
Team: Dudek, Vignal (Riise 73), Carragher, Hyypia, Henchoz, Gerrard, Murphy, Diouf, Kewell (Smicer 73), Owen (Heskey 82), Baros (Pongolle 82).
Subs: Kirkland, Babbel, Heskey, Smicer, Riise, Le Tallec, Pongolle.