Liverpool twice had penalty shouts within the opening eight minutes and both shouts coming off the forearm of Hammers left-back Herita Ilunga.
A Yossi Benayoun cross hit Ilunga's knee before bouncing up onto his right arm was waived away by referee Walton and a few moments later Dirk Kuyt tried to whip in a ball from the same side, but the defender was given the benefit of the doubt when trying to protect his face.
An Albert Rierra effort on 14 minutes brought a good save from visiting keeper Robert Green who stopped the low drive with his feet on the goal-line.
The Reds thought they had taken the lead two minutes later when a Steven Gerrard corner was lofted into the crowded six-yard-box and found the head of Sami Hyypia, but his bullet header flew inches over the bar.
West Ham had one half of their front line to thank for keeping the scores level after another corner from Gerrard was nodded back across the goal by Kuyt and again it was Hyypia stealing in unmarked, but his first-time header was cleared off the line by an unlikely defender in Carlton Cole.
West Ham had failed to create any chances during the match, but out of nowhere it was Liverpool old boy Craig Bellamy who came closest, after picking up the ball inside his own half the Welsh forward was allowed to run at the home backline.
Unleashing from 30 yards, Bellamy's thunderbolt on 37 minutes had Jose Reina beaten and seemed to be flying in, but ball smashed back off the post.
Liverpool should have gone in at the break at least a goal to the good after a Kuyt header in the final seconds of the first 45. Xabi Alonso's deep corner found the Dutchman on the back post, but Green somehow stopped the ball from crossing the line.
The home side started the second half much like they finished the first and it was the Hammers keeper who was called upon once again after a venomous strike from Benayoun was expertly tipped over the bar by Green.
The visitors started to find more space and string one or two passes together and an unchallenged run from Scott Parker led to a neat one-two with Bellamy, but Parker's lacklustre shot was always trickling wide.
A training ground free-kick from Gerrard to Alonso found the Spaniard on the edge of the box, but despite connecting well with his first-time volley, Green was not troubled by the rising effort.
The longer the game went on with the scores level the more nervous the Reds became and a Bellamy corner on 68 minutes was driven to the near post and met by Cole, who managed to get in front of his man, but his header was powered inches wide.
Desperately searching for the opening goal, Rafa Benitez's men piled forward and after just missing tapping in at the back post from a Hyypia header, Kuyt had another opportunity to steal the points with two minutes left on the clock, but Green was on hand once again to keep his side in it.
The visitors could have won it in added time when substitute Luis Boa Morte was played in by Bellamy, but his first touch of the game took him wide of goal and his effort didn't trouble Reina.