The visitors almost took a shock lead in the fourth minute as the sides fought out a goalless first half, but David N'Gog's shot on 52 minutes broke the deadlock, while Yossi Benayoun's 65th-minute strike put the match beyond doubt.
The result gets Livepool back to within four points of Premier League leaders Manchester United, albeit having played two more games than their rivals.
Yet for a side relatively starved of good results in recent weeks, the result - and the impressive manner in which it came - was an enormous relief.
Liverpool's desperation to get themselves back on track was written all over the face of manager Rafael Benitez as the match kicked off, but just four minutes in to the game the home side should have been a goal down.
A long through-ball found Kenwyne Jones - who had sprinted up from within his own half - out in the open, unmarked and clean through on Pepe Reina. The striker took his time lining up the shot - but incredibly, when it finally came, the shot was a dreadfully poor effort to Reina's right that was saved simply.
