A panel of judges including LMA chairman Howard Wilkinson, Sir Alex Ferguson, Joe Royle and Barry Fry, cast their vote and nominated Jürgen Klopp's men for the weekly award.
In guiding the Reds to three points, Klopp became the first manager in 19 years to record back-to-back away victories over Chelsea in his first two seasons.
Dejan Lovren opened the scoring for the Reds with a superb finish, while the goal of the game came from captain Jordan Henderson, who curled home a 30-yard drive to make it 2-0.
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Although Diego Costa pulled a goal back, the Reds were not to be denied as they claimed another crucial away win.