Baros and Morientes had the chance to further their budding understanding, with Igor Biscan taking his place ahead of Didi Hamann, who returned from suspension, and Steve Finnan lining up against his old club.
The visitors, who were unbeaten in their last eight games, made only one change from Wednesday's draw at Aston Villa with Carlos Bocanegra coming in at the back for Moritz Volz.
The Reds picked up as they left off against Charlton with some slick, high tempo passing raising the decibel level on The Kop in the early stages.
Benitez's style appears to be the antithesis of Houllier's lumbering side and the difference is instantly noticeably by the atmosphere. It's been a tumultuous season, but the Anfield faithful are enjoying their football again.
They were given more reason to cheer after just nine minutes when a delightful cross from the rejuvenated Luis Garcia was met with a majestic leap by Morientes – his first goal at Anfield.
Amazingly Fulham were level six minutes later as Andy Cole nodded home his tenth goal against the Reds from a Luis Boa Morte centre after poor play from Steven Gerrard. It was another sign of the fighting spirit that earned Chris Coleman's side an unlikely point against Villa in midweek.
Former Everton star Tomasz Radzinski then wasted a golden chance to add another headed goal, but he diverted Mark Pembridge's corner wide as the Reds, and Gerrard in particular, went back into their shell.
Morientes' class almost told again on 35 minutes as a delightful back-heel released Djimi Traore from a blind alley. His cross was missed completely by John Arne Riise before Biscan tested Edwin Van der Sar with a low drive.
Some fine work from Baros after the interval settled the home side's nerves and he almost regained the lead for Liverpool but couldn't latch onto Riise's knock-back.
Gerrard blasted a 20-yard half-volley over the bar, but the Reds were struggling to penetrate an insular Fulham back line who marshalled Baros and Morientes with great efficiency.
Fulham continued to unsettle the home side, utilising the pace of Cole, Boa Morte and Radzinski to exploit a sluggish Liverpool backline, but failed to test Dudek.
The Reds emerged from a sticky 15-minute spell to regain the lead on 64 minutes when Hyypia met Gerrard's delightful cross with the deftest of touches for yet another headed goal.
It was all Liverpool from that point onwards. Gerrard regained confidence and the introduction of Hamann for the woeful Biscan gave the Reds a much steadier midfield base.
Hamann, celebrating a new 12-month contract at Anfield, stung the fingertips of Van der Sar with a trademark drive. Baros made sure of the points with a typically dynamic finish, smashing home Riise's centre from six yards.
Baros received a tremendous reception as he was replaced late on by Czech team-mate Vladimir Smicer, making his first Anfield appearance of the season after a knee injury.
Both will be vital to Liverpool if they are to overhaul Everton by the end of the season. All eyes will be on the Anfield derby on March 20th.
MAN OF THE MATCH: Luis Garcia (Liverpool) - The Spanish star has endured an inconsistent season but produced one of his best displays in a Reds shirt to help break down Chris Coleman's resolute side.