Liverpool started well and Coutinho was the instigator of two good chances, the first saw an exchange between him and Shelvey which saw the England U21 midfielder drill a shot at goal only to have it blocked and the Brazilian tried with a solo effort.
The pressure continued as Sturridge had a good sight at goal but the chance was rushed and the ball slipped past the far post but as Liverpool were dominating possession, Fulham broke the deadlock just after the half-hour as the unmarked Berbatov latched onto an exquisite cross from Riether with a cool header into the corner past Reina.
Fulham's lead lasted barely three minutes as Liverpool equalised via a careful but concise pass from Wisdom found Sturridge and he swished past Hughes easily before a pinpoint strike past the ailing Schwarzer sent the 'travelling Kop' wild as it hit the roof of the net.
After the break, Liverpool came out firing on all cylinders as after Enrique replaced Wisdom - he curled in a crisp cross for Sturridge who met it well but the resulting header soared over the bar.
As the hour approached it seemed more likely for Liverpool to score than Fulham and as Coutinho hit a sharp shot, it deflected into the path of Sturridge who made no mistake in slotting a side-footed chance past Schwarzer to give his side a 2-1 lead. The lead could have been by three within minutes but two expert saves from Schwarzer denied Sturridge his hat-trick.
Liverpool sealed the win with five minutes to go as the lethal combination of Sturridge and Coutinho struck again as a super pass from the Brazilian playmaker found the England striker who lifted the ball over the onrushing Schwarzer and into the empty net to secure a well deserved three points for his side.