The Uruguayan curled low and hard past Joe Hart in the 66th minute to restore the Reds’ lead after Yaya Toure had cancelled out a towering Martin Skrtel header.
However, Carlos Tevez cut out a Skrtel pass with 10 minutes remaining and rounded Pepe Reina to clinch a point for the visitors.
Steven Gerrard set the tone for a boisterous Anfield occasion when he surged into the penalty area and smashed a Suarez lay-off wide of Hart’s post after just 30 seconds of play.
The ground was rocking but it was soon to be dealt a sobering blow when Lucas Leiva pulled up in pain and dragged his shirt over his head in frustration. Jonjo Shelvey was on his feet in a matter of seconds and the switch was made.
There was scarcely a moment to dwell on such a loss as an almighty roar went up from the Kop when Raheem Sterling, making his full league debut, killed the ball with one touch and sped towards goal.
Fabio Borini looked to slip it back to him but Pablo Zabaleta appeared to block it with his hand. No penalty given.
The Reds looked lively and hungry for a goal. At the heart of their midfield, Joe Allen was neat and industrious. The 22-year-old broke down City moves all over the park muscling players off the ball, cutting out passes and putting his foot in.
It was one of his interceptions that instigated the first real Liverpool opportunity of the game. Glen Johnson fed Sterling, who stepped over twice and sent a cross crashing towards the near post, where Borini was arriving. The Italian poked agonisingly wide.
Moments later it looked as though all the Reds’ good work was about to be undone.
An incisive City break saw Tevez fed in on goal. The Argentine rounded Reina on the touchline and, from the tightest of angles, clipped the ball across the face of goal.
It bobbled across the goal-line and struck the far post as Anfield held its collective breath.
Then, in a split second that seemed to last for an eternity, Gerrard, Sebastian Coates and Martin Kelly, who had all converged around the loose ball, realized no City player was arriving to turn it home and allowed Reina to smother the danger.
But the game refused to stand still. It ebbed and flowed and the Anfield crowd followed suit.
Samir Nasri whipped a tantalising free kick into a dangerous area at one end while Sterling tinkered with the ball at the other. Mario Balotelli nipped in to steal possession from Coates in front of the Anfield Road while Borini’s stinging effort on goal was deflected into the Kop by Vincent Kompany.
Suarez sent Hart sprawling across his goal-line with a snapshot that struck Kolo Toure on the head before it could fly into the corner of the net. Balotelli rocketed the ball over Reina’s bar on the half-hour mark.
Then Borini, alert and on the move, gestured to exactly where he wanted a pass placing in the City penalty area and Gerrard obliged, rolling the ball out of his feet before whipping it into the heart of the City box. Kompany had to stretch to deflect it onto the roof of the net.
Within seconds Anfield had erupted. The resulting corner was arrowed into the danger area and Skrtel blazed a trail between a cluster of City bodies and thundered the ball past Hart with his head.
If Kompany thought he had been astute in electing to have the Reds attack the Kop in the first half he might have thought otherwise as he watched the famous old stand transform into an almighty blur of swirling scarves and flailing arms as the Liverpool players celebrated to his right.
Halftime reached, it was all going according to plan for the home side.
It almost got a whole lot better when Borini robbed Zabaleta of possession and raced towards goal before sliding a pass into Suarez, who could only poke wide.
However, 62 minutes in, Tevez snuck in behind the Reds defense and crossed into the middle. Liverpool failed to clear their lines and Toure smashed the ball home.
Within minutes, Anfield was shaking to its foundations once again as Gerrard shot from the edge of the box and substitute Jack Rodwell blocked with his arm.
Andre Marriner signalled a free kick and Suarez stepped up to bend the ball low into the corner of Hart’s net.
But in the 80th minute Tevez seized onto a Skrtel back pass, rounded Reina and rolled the ball into the back of an empty net to equalize.