The match was threatened earlier in the week by a proposed strike on the London Underground - and Brendan Rodgers' six-match unbeaten league run looked in serious danger of ending on several occasions in west London.
Rene Meulensteen's side produced a performance that belied their position at the bottom of the Premier League, only for them to twice see leads pegged back and then Reds skipper Gerrard strike home in stoppage time.
It was a fine win but one in which Liverpool failed to get anywhere near the heady heights reached in Saturday's 5-1 mauling of Arsenal, falling behind after just eight minutes.
Kolo Toure, guilty of gifting West Brom a 1-1 draw 10 days ago, could only watch on in horror when he sliced a Kieran Richardson cross into his own goal.
Fulham continued to impress but were undone as half-time approached by a wonderful first-time Gerrard through ball, which found Daniel Sturridge to net his eighth goal since returning from injury.
While Liverpool were somewhat fortunate to go in level at half-time, they began the second half with renewed vigour and Luis Suarez rattled the far post as the Whites looked increasingly unsteady.
Fortunately for them, Martin Skrtel was looking even more shaky and his defensive mistake allowed Manchester United academy graduate Richardson to net from close range.
The lead did not last long, though, as Philippe Coutinho sent a fine shot past Maarten Stekelenburg via a slight deflection off former Everton defender John Heitinga.
Fulham looked good value to follow up their thrilling 2-2 draw at Manchester United with another point, only for Sascha Riether to foul Sturridge, allowing Gerrard to fire home a stoppage-time winner from the spot.
Few expected Fulham to suffer a ninth home loss of the season given the way they flew out of the blocks.
Less than a minute was on the clock when Lewis Holtby sent a lovely chipped ball over to Darren Bent, who played in the overlapping Ryan Tunnicliffe for a strike that stung the palms of Simon Mignolet.
Dan Burn headed over as Fulham continued in the ascendancy, with their early endeavours rewarded with just eight minutes on the clock.
Holtby's exquisite through ball put Richardson behind Skrtel, with the former United man's cross comically turned into an own goal by Toure.
It was quite the start by the Whites, for whom things came close to improving moments later as Holtby met a Darren Bent knock-back with a half-volley that flew inches wide.
Liverpool were struggling to quell Fulham's intensity, but with Suarez in attack it would not be long before Stekelenburg was called into action.
The Netherlands goalkeeper denied his former Ajax team-mate after impressively wriggling free to turn on target, before thwarting the Reds striker's cheeky attempt at a lob.
Stekelenburg saved Steve Sidwell's blushes after his woeful backpass almost put Suarez through on goal, with Sturridge and Coutinho wasting chances before Fulham regrouped.
Former Liverpool left-back John Arne Riise and Sidwell saw shots blocked either side of a Bent headed as the hosts upped the ante, coming closest when Holtby played a neat one-two with William Kvist and continued to fire into the side-netting.
They were missed chances the home side were made to rue four minutes before half-time.
Getting back on his feet after slipping just inside the Liverpool half, Gerrard played a wonderful first-time ball with the outside of the right boot that split the Fulham defence open and found Sturridge to coolly slot home off the inside of the far post.
The England internationals both came close to adding to that before half-time, from which they returned with Suarez whipping a free-kick just wide of the far post.
The Uruguay international was soon back in action again, first lashing across the face of goal before striking the post after turning his man on the edge of the 18-yard box.
It looked only a matter of time until there was a goal, but few expected it to come from Fulham.
A hopeful, if impressive, Sidwell shot from his own half was all the Whites had to show until the 63rd minute, when Liverpool gifted Fulham another lead.
Skrtel could not clear a Riether cross from the right, wiping out team-mate Jon Flanagan as the ball fell kindly for Richardson to bury from close range.
However, the lead was not to last as Coutinho showed impressive skill and poise to burst into space and strike, via a slight deflection of Heitinga, past Stekelenburg
The Fulham goalkeeper was soon forced off after taking a bad knock in denying Suarez, with his replacement David Stockdale seeing Coutinho struck just wide before substitute Joao Teixeira fired over on his debut.
And, just as it looked like the west Londoners would take a deserved point, Riether was adjudged to have taken down Sturridge in the box.
Dowd pointed to the spot and Gerrard smashed home the spot-kick in front of the raucous visiting fans, who almost had another to celebrate when Teixeira struck over.