The Spain international side-footed home the simplest of efforts in the first half from Raul Meireles' pass and then fired home a second in the 90th minute after the Portugal midfielder had made it 2-0 with a spectacular volley.
Torres is now Liverpool's leading scorer with nine - all in the Barclays Premier League - after hitting three in his last three matches.
"It is the best [performance] since I've come in, the way he worked," said Dalglish of Torres.
"It was not just his goals it was the work-rate he put in. He really helped us by closing the goalkeeper down.
"The keeper kicks it the full length of the pitch and that is a great asset for him and we asked him to nullify that and he did. He showed he wanted to do something and he did it. The goal he scored last week (in the defeat at Blackpool) wouldn't have done him any harm so I'm very happy."
Source: PA