The Reds ended an 11-year run of no wins on Gunner soil by capitalizing on the fact that Arsene Wenger's men were reduced to ten with 20 minutes remaining.
Emmanuel Frimpong's red card on debut kicked Kenny Dalglish's charges into gear with an own goal from Aaron Ramsey and a late strike from Luis Suarez doing the damage to a hapless Arsenal outfit which is in desperate need of some star quality following Cesc Fabregas' departure.
In other Premier League matches, Newcastle United won the first Tyne-Wear derby of the season against Sunderland 1-0 thanks to Ryan Taylor's 62nd minute free-kick as Black Cats defender Phil Bardsley saw red.
In Birmingham, Aston Villa brushed aside a struggling Blackburn Rovers outfit 3-1 thanks to goals from their three-prong attack of Gabriel Agbonlahor, Emile Heskey and Darren Bent whilst Morten Gamst Pedersen gave Steve Kean's men some hope but it wasn't enough to deny Alex McLeish his first lot of three points at Villa Park.
Everton kicked off their season with a disappointing 1-0 result against QPR, who secured their first maximum haul in the top flight since 1995-96 thanks to Tommy Smith's first half goal, as Swansea City grabbed a first-ever Premier League point with a scoreless draw at home with Wigan Athletic.
And in the final match of week two's opening day, Chelsea came from behind to defeat a plucky West Bromwich Albion 2-1 with second half goals from Nicolas Anelka and Florent Malouda after Shane Long opened the scoring for the Baggies after just four minutes.
Sunday sees Norwich City host Stoke City at Carrow Road, Wolves at home to Fulham and Bolton take on Manchester City at Etihad Stadium whilst reigning champions Manchester United meet Tottenham at Old Trafford on Monday night.