After Raul Meireles's 47th-minute opener the Uruguay striker, a deadline day capture from Ajax Amsterdam, joined the fray in the 63rd minute and tucked in the second goal to secure seventh-placed Liverpool's third successive win and take them within two points of Sunderland.
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It was a bad night for Manchester City as they could draw 2-2 only at Birmingham City. Tottenham Hotspur gained ground as Peter Crouch's early goal earned them a 1-0 win at Blackburn Rovers.
In the furore surrounding Fernando Torres's 50 million departure and the 36 million pounds arrival of his replacement Andy Carroll, Suarez sneaked somewhat under the radar despite, for a few minutes at least, being Liverpool's record signing.
With Carroll still nursing a thigh injury and Suarez not having played for two months, Dalglish went with his tried and tested troops who, after a battling first half, forged ahead with Meireles's shot.
"Everyone's pleased for Suarez, that's fantastic for him and great for the supporters," manager Kenny Dalglish told Sky Sports.
"He's not trained with the players yet so it's something to look forward to when he joins the lads. That's three wins and three clean sheets so it's a good night's work."
Carlos Tevez put City ahead after four minutes, Nikola Zigic levelled after 23, Aleksandar Kolarov restored City's lead with a great free kick late in the first half but a Craig Gardner penalty in the 77th earned the hosts a deserved point.
"I'm disappointed with me
