It was not the most notable of performances, although there were plenty of spells of good football from the hosts, as John Pantsil's second-half own goal divided the teams.
But the Reds registered back-to-back wins for the first time since early November to move up to seventh, within six points of fifth-placed Tottenham, and maintain the feeling of optimism which arrived when Dalglish replaced Roy Hodgson earlier this month.
The last time the legendary Scot faced a Fulham team at Anfield he was player-manager on the occasion of a 10-0 League Cup victory in September 1986 against the then third-division side - and he did not even score.
There was to be no repeat of those fireworks, understandably considering Liverpool's still fragile form and the Cottagers' precarious position.
Until Pantsil put through his own net the main talking point was the goal Fernando Torres had disallowed after just six minutes.
Liverpool's last match, the 3-0 win at Wolves, had prompted much debate - and subsequent sexism controversy - about female referee's assistant Sian Massey.
On that occasion she made the correct call in not flagging Raul Meireles offside for the Reds' opening goal at Molineux.
Male counterpart Mick McDonough was not so accurate as he wrongly ruled the Spain international was offside before he slotted Meireles' through-ball past David Stockdale.
Fortunately for the assistant referee, Pantsil prevented him making the headlines.
Portugal international Meireles was man of the match at the weekend and he started brightly again as he kept the advanced midfield role even on captain Steven Gerrard's return after suspension.
It was he who got on the end of Martin Kelly's right-wing cross to direct a low header goalwards which the goalkeeper turned around his post.
Stockdale was called into action again in the 25th minute when Glen Johnson, playing at left-back, cut inside to unleash a right-footed shot which the keeper tipped over.
Clint Dempsey forced Jose Reina into a low save just before the half-hour but the Spain international should not have been given a chance seconds later when Andrew Johnson cut the ball back to the penalty spot but Moussa Dembele hit his shot straight at the goalkeeper.
Daniel Agger fired a low 30-yard drive wide and Torres headed over from Kelly's cross in added time at the end of the first half as the hosts failed to make their dominance pay.
Maxi Rodriguez had a shot blocked by Aaron Hughes but when a cross was swung back into the area the Argentinian wasted his free header with an aimless looping effort.
But that was forgotten when Liverpool took the lead in the 52nd minute.
Dirk Kuyt's interception of Dempsey's pass touched the ball into the path of Torres on the edge of the penalty area and he unleashed a shot which deflected off Brede Hangeland and rebounded back off the post.
Pantsil and Stockdale got in the way of each other in the resulting melee with the defender, under pressure from Meireles, slicing an attempted clearance over his own goalline.
The Fulham right-back tried to make amends when his cross picked out Dempsey but the American volleyed straight at Reina.
Meireles' quick counter-attack from Reina's throw almost brought the second goal as his attempted pass to Rodriguez deflected off Hughes and had Stockdale scrambling at the foot of his left-hand post to recover.
The Fulham centre-back proved equally effective at the other end as his header forced Reina into a full-length dive to prevent the ball creeping inside the post.
Seconds later Meireles displayed his rarely-seen defensive duties by hacking Hangeland's header off the line with the goalkeeper beaten.
Liverpool hung on, something they have struggled to do in the past, as Dalglish's influence continued to be felt.
At the final whistle the PA system played Somewhere Over The Rainbow. Optimism is definitely growing at Anfield.
Liverpool Reina, Kelly, Skrtel, Agger, Johnson, Meireles,Poulsen (Aurelio 80), Kuyt (Shelvey 66), Gerrard, Maxi, Torres.
Subs Not Used: Gulacsi, Cole, Pacheco, Wilson, Ngog.
Goals: Pantsil 52 og.
Fulham Stockdale, Pantsil, Hughes, Hangeland, Baird,Duff (Gera 63), Sidwell, Murphy, Dempsey, Dembele,Andrew Johnson.
Subs Not Used: Etheridge, Kelly, Salcido, Kamara, Greening,
Ref: Lee Probert (Wiltshire).