Bellamy returned to action after being withdrawn from the squad for Sunday's clash with Manchester City on passionate grounds.
The 32-year-old was mourning the loss of friend Gary Speed and stood with his head bowed during the minute's applause held at Stamford Bridge in remembrance of the Wales manager.
Kenny Dalglish: "Craig is a fantastic footballer who had a hugely disappointing day on Sunday. He regarded Gary Speed as a mentor.
"It was great for the wee man, making the first goal. For the second he took the free-kick. He told Martin to leave it, it was going in!
"I don't know if we took Chelsea apart but we were delighted with the way we played. We've had a good day and we deserved to go through.
"The way we're progressing is more significant than reaching the semi-final of a cup that's been cheapened by the actions of the people who run it.
"But that doesn't mean to say we wouldn't love to win it. We've got our reward and we'll look forward to the next game.
"Three teams in the quarter-finals have problems with fixtures. Do us a favour.
"I'm not clever but I think I could have avoided that. The solution is to get someone a brain."