Just moments after Sebastian Larsson had hit the bar for the hosts, Daniel Sturridge controversially gave the away side the lead, appearing to use his arm to nudge the ball goalwards, before Suarez doubled the advantage just eight minutes later.
Emanuele Giaccherini netted immediately after half-time as Sunderland hinted at a comeback, but, in pushing forward for an equaliser, they were stung on the break as Liverpool's Urguayan frontman grabbed his second goal late on.
Liverpool named an unchanged team from their narrow defeat against Manchester United in the Capital One Cup, with Rodgers choosing to stick with the 3-5-2 formation that served his side well at Old Trafford.
|By Ian Joseph Capasso
Liverpool take the three points back to Merseyside and go second on the table with a 3-1 victory over in-crisis Sunderland.
Luis Suarez bagged a brace in his return to Premier League action and Daniel Sturridge was involved in each of the Reds' three goals to lead Brendan Rodgers' men from the front.
The Black Cats will be disappointed as they turned in a decent performance, but remain at the bottom of the table with only one point after recording their fifth loss of the season.
Suarez was handed his first league start after serving his 10-match ban, and he made an instant impression on the match as he drove narrowly wide from the edge of the area early on.
Liverpool had the ball in the Sunderland net in the first 10 minutes, but Martin Skrtel saw the linesman's flag rightly raised for offside after he had side-footed the rebound from a Steven Gerrard free-kick into the roof of the goal.
An entertaining midfield scrap ensued after that disappointment for Liverpool, but Sunderland were the next to go close to scoring amid the melee as Larsson curled a brilliant effort onto the bar with former team-mate Simon Mignolet stranded.
The visitors had ridden their luck to remain level, and were the recipients of yet another slice of good fortune at the other end of the pitch moments later. Gerrard found Sturridge from a corner and, having misjudged his attempted header, the England international used his arm to prod the ball over the goalline and give Liverpool the lead.
Just eight minutes later, Rodgers' side had their second, and it came - perhaps inevitably - from returning forward Suarez. A fabulous cross-field ball from Gerrard allowed Sturridge to make ground on the right-hand side, and the striker's pass across goal provided his Uruguayan colleague with a tap-in from close range.
Liverpool had little trouble in taking their two-goal lead into the break, but the away side received a rude awakening early in the second as Sunderland pulled one back. Mignolet failed to keep hold of a Ki Sung-Yueng effort from the edge of the box, and Giaccherini reacted quicker than the visitors' defenders to poke the ball home.
The goal buoyed Sunderland's fans, with the increased noise inside the Stadium of Light adding vigour to the hosts' counterattacks.
But Liverpool looked the bigger threat, and they came close to doubling their lead on two occasions as Victor Moses' inswinging cross drifted narrowly wide before Suarez should have done better in getting onto a cross from the left.
The 26-year-old eventually got his second, however. With Sunderland committing men forward, Liverpool were able to break; Sturridge darted into the box and unselfishly squared the ball to Suarez, who passed the ball into the back of the net to wrap up the victory.