Liverpool 3-0 Sunderland
Joe Allen and Glen Johnson also saw goals disallowed in a game that the reds dominated from the opening minute.
New signing Daniel Sturridge was amongst the crowd as he watched Suarez and Sterling torment the Black Cats defence.
Astonishingly this is only the first time this season that Brendan Rodgers has seen Liverpool win two consecutive Premier League games. Stewart Downing saw an early free kick pushed away for a corner from Mignolet.
Downing, although guilty of giving the ball away a number of times, seemed to be continuing his slight improvement in form - helped by Glen Johnson behind him at left back - Andre Wisdom handed the right back role.
Jordan Henderson was once again preferred over Joe Allen in the midfield and distributed the ball well to the wide men.
In the 19th minute Suarez sent a well placed ball over the defence to Raheem Sterling who showed impressive composure to lob over the Sunderland keeper and give the reds their lead.
Seven minutes later Gerrard released Suarez, who stayed on his feet after being fouled by Cuellar, and smashed in a fine shot to double Liverpool's lead.
Pepe Reina was called in to action to stop a Kilgallon shot from deep inside our area - Liverpool still being troubled by crosses deep in to the box.
Suarez doubled his tally in the 52nd minute - again from a Gerrard pass.
Liverpool continued to dominate the game and both Joe Allen and Glen Johnson saw goals in front of the Kop ruled out for offside.
No matter. Liverpool move up to 8th in Brendan Rodgers' 21st Premier League game in charge of Liverpool.
Liverpool face a tough set of fixtures in the next few weeks so will be hoping that Sturridge can combine well with Sterling and Suarez - who were both excellent tonight.