Suárez netted a 13th-minute opener as he scooped a finish past Crystal Palace goalkeeper Julian Speroni before England striker Sturridge netted his sixth Premier League goal of the season minutes later.
Liverpool captain Steven Gerrard polished off an efficient first-half performance with his 99th top-flight goal from the penalty spot after Raheem Sterling had been dubiously pulled back by Dean Moxey.
The Reds took their foot off the accelerator in the second half and Palace rallied as half-time substitute Dwight Gayle nodded in a consolation goal with 14 minutes remaining.
“They were exceptional today. Their combination play was outstanding and they are right up there with the best in this league,” said Rodgers.
Meanwhile, Liverpool striker Sturridge admitted he was in the form of his life after scoring his eighth goal of the campaign in all competitions.
“I have been given an opportunity to play in a position I’ve played all my life,” said Sturridge.
“The manager has given me a chance at Liverpool and I thank him for giving me the opportunity to show the world what I can do.”
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