The attacking duo both scored in the comprehensive victory at Anfield, taking their record to 12 goals between them in nine Premier League appearances.
Liverpool now move to the summit of the table with Arsenal not due to play until Sunday.
The hosts made the perfect start as Suarez first slotted home after neat interplay with Jose Enrique before a superb solo effort from Sturridge doubled the advantage on 17 minutes.
Steven Gerrard then added a third from the penalty spot six minutes before half-time to essentially wrap up the points, although Dwight Gayle grabbed a consolation with a near-post header in the second half.Brendan Rodgers brought in Raheem Sterling for the suspended Lucas Leiva, while Ian Holloway named Jason Puncheon and Cameron Jerome in Palace's starting XI.
Liverpool made the brighter start but could have been behind had Jerome done better with his eight-yard header from Puncheon's lofted cross.
It was one-way traffic from that early scare, however, as two goals in four minutes put the hosts in control.
Suarez first played a neat one-two with Enrique in the box and, despite slipping, managed to keep his balance to slot home beyond Julian Speroni.
The home fans were celebrating again in the 17th minute with a fine individual effort from Sturridge.
The England international striker tormented Joel Ward on the left before firing powerfully across goal into the far corner.
Palace pushed to get back into the game and Jimmy Kebe took ownership of a long ball before nudging an effort towards goal that Kolo Toure cleared off the line.
But Liverpool then made it 3-0 from the penalty spot in the 39th minute. Sterling played a one-two with Suarez and was tugged down by Dean Moxey just inside the area.
Gerrard duly dispatched the spot-kick hard to the Speroni's right.
Soon after Suarez once again teased the Palace defence and crossed for Victor Moses from the byline, but the Chelsea loanee saw the ball flick off his foot and hit the crossbar.
Mamadou Sakho nearly extended Liverpool's advantage immediately after the break when he powered a header wide from Gerrard's corner.
Liverpool continued to dominate possession but were frustrated in their attempts for a fourth.
Gayle wasted a great chance to reduce the deficit when he hit a fierce 20-yard strike over the bar, but with 15 minutes remaining Palace did pull one back as the forward flicked home a near-post header from Jose Campana's header.
Sturridge then hit the post in the closing stages as Liverpool looked good value for a victory that moves them back to the top of the Premier League and consigns Palace to a fourth consecutive league defeat.