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.
Manchester United, who beat Aston Villa 3-1 on Tuesday, lead the way with 54 points, five ahead of Arsenal. Manchester City have 46, Chelsea 44 and Spurs 41.
At the other end of the table, West Ham United, helped by a goal by loan signing Robbie Keane, won 3-1 at Blackpool to climb off the bottom.
Daniel Sturridge, another deadline day loan from Chelsea to Bolton Wanderers, scored the only goal in stoppage-time to earn his new club a home win over Wolverhampton Wanderers.
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.
Suarez was given a rapturous welcome when he came on and the fans were soon singing his name even louder after he ran clear and slotted his first goal, helped by a miscued clearance attempt by Andy Wilkinson.
MANCINI DISAPPOINTED
"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."
Manchester City twice lost the lead at St Andrews and, after a poor second half, were hanging on against a Birmingham side who had one only one of their last eight league games.
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.
Having lost at Aston Villa last time out City are looking more likely to be embroiled with a battle with Chelsea and Spurs for fourth than fighting their neighbours for the title.
"I'm disappointed with me
