Earlier, West Ham's Luis Boa Morte twice missed from six yards out while Xabi Alonso headed on to his own bar.
Lucas Leiva missed from eight yards for the Reds while Fernando Torres' shot was saved by Robert Green.
The result must have buoyed West Ham boss Alan Curbishley whose best-laid plans to frustrate Liverpool did not go awry.
Although the Reds had not won in the league for over a month they had beaten the Hammers in their last seven meetings.
Curbishley said afterwards: "It's tremendous - if you're going to get a penalty and score then it's a great time to do it.
"Week in and week out we've put in a lot of effort - the squad have a fantastic attitude and full credit goes to them.
"We've lost three games in the last 16 and that's gone unnoticed."
Liverpool manager Benitez said: "We had chances but couldn't take them.
"We started really well and in the second half we had a lot of possession and to lose following a counter attack in the final minute is disappointing.
"For them to score from a penalty so late on was terrible. We now need to think about the next game."