Last night, however, they were intent on capitalising on any advantage with the irrepressible Uruguayan giving Sunderland centre-back Carlos Cuellar a torrid time.
It was from a Cuellar foul on Suarez that Downing fired a 12th-minute warning to the visitors, forcing a flying save from Sunderland goalkeeper Simon Mignolet with a curling free-kick.
But Liverpool only had to wait another seven minutes for the opener, Suarez showing great control and vision to create the opportunity by taking the ball on his chest on the halfway line and hooking a pass over his head into space for Sterling to chase.
The 18-year-old then showed great composure to bide his time before lobbing the ball over Mignolet and into the goal.
Sterling initiated the move that earned Liverpool their second seven minutes later when challenging for a high ball near the halfway line.
Gerrard leapt on the loose possession and prodded the ball forward towards Suarez, who benefited from a good advantage by referee Phil Dowd after being impeded by Cuellar and advanced into the area before finishing expertly beyond Mignolet with the outside of his right foot.
It was almost three moments later, a sliding Downing almost turning in Henderson’s deep cross at the far post.
Sunderland were not without their chances. Shortly after going behind, Steven Fletcher found James McClean in space 10 yards from goal but the winger spurned a great opening by shooting wide.
And towards the break, Reina pulled off a fine save to repel Fletcher’s shot from an Adam Johnson cross before scooping the ball wide before Matt Kilgallon could pounce.
Any Sunderland resistance ended on 53 minutes. Three minutes earlier, a brilliant flicked pass around the corner from Suarez put Sterling in again but the youngster was too cute with his finish and didn’t trouble Mignolet.
But when Gerrard’s excellent long diagonal pass split the Sunderland centre-backs, there was never any doubt that once it reached Suarez, the ball would end up nestling into the Kop goal.
There could have been more. A fine save from Mignolet prevented Gerrard’s volley from being deflected in by Glen Johnson, with the goalkeeper’s feet then denying Suarez a hat-trick.
A goalbound shot from substitute Allen ricocheted off Danny Rose and flew over, with the midfielder hitting into the side-netting late on and then seeing an effort chalked off by a debatable offside flag.
Maybe Liverpool supporters really can start to dream. Well, a little bit anyway.
MAN OF THE MATCH. Luis Suarez. Brilliant.