Suarez, making his first Anfield appearance of the season after completing a suspension for biting, set Liverpool on their way to their fifth league victory with an early improvised finish.
England forward Sturridge, who has now scored or assisted 16 goals in his last 11 league appearances, made it two with a fine solo goal, and Steven Gerrard's penalty - his 99th Premier League goal - made it three before halftime against struggling Palace.
In the early kickoff at the Etihad Stadium, Alvaro Negredo and Sergio Aguero scored to help City come from behind to beat Everton 3-1, easing the disappointment of their home loss to Bayern in the Champions League on Wednesday.
French striker Loic Remy gave Newcastle United's under-pressure manager Alan Pardew some relief by scoring twice in a 2-1 win at Cardiff City and Fulham did the same for manager Martin Jol, edging past Stoke City 1-0 after Darren Bent's 83rd-minute winner.
Hull City and Aston Villa played out a goalless draw at the KC Stadium.
Champions Manchester United will be aiming to avoid a third successive defeat when they face Sunderland in Saturday's late kickoff.
Arsenal, Tottenham Hotspur and Chelsea all play on Sunday.
(Editing by Ed Osmond)
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