Danny Murphy also had a good shot from the edge of the box parried by Sorenson on 16 minutes.
Diouf came to Liverpool's rescue a few minutes later, clearing the ball off the line when Whittingham had a chance to put the home side ahead.
On 34 minutes Mellberg and Sorenson collided allowing the ball to roll just wide of the Villa post with Michael Owen in pursuit.
Villa started the second half better and Dudek had to make three very important saves, from Angel, Delaney and Vassell, to keep Liverpool in the game.
Milan Baros replaced Heskey after the big centre-forward took a knock on the calf.
On the hour mark Angel hit a fabulous free-kick from outside the box, beating Dudek but not the post.
Villa continued to control the game, keeping possession, having the best of the chances and forcing Liverpool to chase the game.
But Steven Gerrard almost broke the deadlock in a goalmouth scramble in the Villa area and was almost booked for a reckless challenge in the process.
After more Villa pressure Liverpool counter-attacked with Baros, Diouf and Owen, but the Czech striker's shot went straight to the keeper.
Liverpool regained their composure in the final ten minutes but Villa defended in numbers and kept them at bay.
John Arne Riise fired a header from a late corner and Owen failed to capitalise from the rebound.
The game ended goalless, giving both sides their first points of the season.
Team: Dudek, Carragher, Henchoz, Hyypia, Riise, Kewell, Diouf, Gerrard, Murphy (Biscan 87), Owen, Heskey (Baros 58).
Man of the match?