© PA Photos
Suarez almost doubled this lead ten minutes before the break but his 25-yard effort clipped the side of the post before going wide.
The Reds came close again on the stroke of half time when Sterling found Glen Johnson, but the full-back could only steer his shot straight at the keeper.
Sterling came close to grabbing a second one minute after the restart, having been found by Suarez once more, but his shot was straight at Alex McCarthy.
Jobi McAnuff and Steven Gerrard both had efforts well-saved at either end of the field as the game began to open up, but neither side could find the winner as Rodgers picked up his first Anfield league win as Liverpool boss.