Dirk Kuyt converted from the penalty spot courtesy of a contentious decision from the referee, before Suarez sealed the victory with a sublime strike at the Stadium of Light.
The £50 million duo were named in the starting line-up together for the first time and the Reds' boss was overjoyed with their performance.
“The two lads we brought in during January played together for the first time today and showed a lot of very encouraging signs,” said Dalglish.
“Andy made a fantastic physical effort to play 90 minutes on Thursday and another 70 today. Luis chipped in with a fantastic goal and the two of them showed encouraging signs of what we can look forward to.”
However, Dalglish refused to put a time limit on when the pair will start scoring regularly.
"I don’t think there is a set time for partnerships to form. It either happens or it doesn’t. It was encouraging," he said.
By Jake Svensson
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