The Slovakia defender knew little about his fifth-minute intervention, which came from the first of Fulham’s exceptional counter attacks, as a mostly second-string Liverpool toiled, with Andy Carroll particularly disappointing.
The Reds did have chances to level, their finishing wasteful with Mark Schwarzer not called into any saves of note, but Fulham should have added to their lead, with Kerim Frei hitting the post and Liverpool goalkeeper Doni making outstanding saves from Pavel Pogrebnyak and Clint Dempsey.
The result means Fulham go level on 49 points with eighth-placed Liverpool, who have now only won five of 18 home games this season and slip three points behind Everton, who drew at Stoke City.
Winning away - let alone at Anfield - is not one of Fulham’s strengths, but they tend to do well in May and Liverpool’s home form has been shaky at best this season.
Dalglish’s side were almost insultingly under-strength with the FA Cup final against Chelsea in mind, although the fact they stood to lose most from a Fulham victory means a Premier League charge is unlikely to be forthcoming.
Pepe Reina, Steven Gerrard, Luis Suarez, Glen Johnson, Jose Enrique, Jamie Carragher, Dan Agger, Stewart Downing and Craig Bellamy were all missing from the starting XI, with only Jonjo Shelvey and Jordan Henderson retained as Dalglish kept both eyes on Wembley.
Fulham took an early lead to complicate matters when, on five minutes, Dempsey’s strong run allowed John Arne Riise to torment his former club with a vicious low cross: another ex-Red, Alexander Kacaniklic, got a faint touch, Skrtel unfortunate to divert the ball past stand-in keeper Doni, although Pogrebnyak would almost certainly have scored but for the Slovakian’s intervention.
The visitors were by far the more threatening in the early stages, Doni pulling off a fantastic save to deny Pogrebnyak, whose flying volley almost finished off a sweeping move started by Kacaniklic with Dempsey also involved.
But, midway through the first half, the unfamiliar Liverpool XI started growing into the match, as Dirk Kuyt - linked heavily with Hamburg in recent weeks - pinged a volley just wide.
Brede Hangeland had to clear Shelvey’s low drive off the line after Schwarzer flapped at a high ball, while Maxi Rodriguez headed over after a powerful flick-on by the busy but poor Carroll.
Carroll was having a surprising amount of joy in the air given Hangeland’s presence, and one such flick allowed Shelvey to hold the ball up for Maxi, who again put his finish off target.
Shelvey was also doing well, popping up on the left to blast a drive across goal that Schwarzer palmed away, while Fabio Aurelio - making a rare start - put in a fine cross that Carroll once more beat Hangeland to, but the England striker could only head at Schwarer.
It was more of the same at the start of the second half, although Fulham had the best early opportunity when Dempsey’s powerful header flew just wide.
That seemed to provoke the hosts into action as they started a sustained assault on the Whites goal: Maxi could have gone down when tugged by Aaron Hughes but he showed great honesty to stay on his feet, allowing Stephen Kelly to block the finish; Carroll, meanwhile, failed to anticipate Hangeland missing a cross, the ball dropping in front of him when he should have been alert to pounce.
Fulham were still dangerous on the break, Frei firing a warning shot off the pos with a superb effort from range after Dempsey picked him out, while Riise forced a smart stop from Doni after Moussa Dembele split the defence with a now-typical pass.
Similarly, Liverpool were still wasteful, as Carroll headed wide from a good position, blaming everyone but himself for getting his angles wrong, before mis-hitting his finish as he slipped following a smart turn past Hangeland.
Fulham sensed the danger so opted for a more cautious, possession-based finale and it almost reaped dividends when Danny Murphy brilliantly turned to find Frei, whose through-ball sent Dempsey clean through: you would bet property on the American to score, but he telegraphed the low finish which was kept out in style by Doni.
In their enthusiasm to equalise Liverpool - who brought on exciting youngster Raheem Sterling for a 15-minute cameo - were making defensive misjudgements. Skrtel almost handed Fulham a second with a woefully undercooked back-header, but Doni made himself big to deny Dempsey.
Down at the other end Sterling was making a name for himself with some mazy runs and whipped crosses, but his team-mates were not exactly showing for him and Fulham held on for a historic victory and one that leaves them one win short of seventh with two games left.