Gerard Houllier's men certainly needed this Anfield victory with their rivals for the coveted fourth spot in the Premiership - Chelsea and Everton - also winning.
The margin of victory could have been far more comfortable had it not been for Fulham goalkeeper Maik Taylor. And although Liverpool were short of flair they were convincing and workmanlike - and far too good for an increasingly dispirited Fulham side who are still not safe from the drop.
The Reds again had to thank Michael Owen for his 23rd of the season, with much maligned England colleague Emile Heskey netting the first goal.
Owen returned for Liverpool following a back injury, with boss Houllier opting for three strikers after losing Danny Murphy to a neck injury in the warm-up.
It meant Vladimir Smicer got a late call and Neil Mellor was added to the bench.
Liverpool's reshuffle caused by Murphy's late withdrawal meant Heskey was again moved from his natural front role, this time to wide on the right.
The hosts were denied a dream start by a linesman's flag in the fourth minute when Owen hooked home after Heskey nodded down a John Arne Riise long throw.
And after a scrappy start, Liverpool slowly turned on the pressure, and Taylor was forced into constant action to keep Fulham in contention. Baros, an unlucky victim of the tactical reshuffle which followed Sami Hyypia's red card last weekend in the 4-0 mauling at Manchester United, could have had a first half hat-trick.
However, Taylor made a brave save to his left to turn an effort round a post and dived at Baros' feet when the Czech was clear, before Baros' control let him down with the goalkeeper helpless a matter of yards away.
Fulham rarely threatened, although Reds' keeper Jerzy Dudek just got his fingertips to a fine Sean Davis drive after the midfielder had cleverly made space on the edge of the box for a low drive.
Owen had an excellent game, dropping deep and taking on defenders.
One stunning run from 40 yards took him past three men and forced Taylor into a fine block, then another long-range drive forced the goalkeeper to beat away.
But Liverpool's pressure finally paid dividends on 36 minutes when Riise's free-kick from the right dropped into the area, was nodded on by Smicer, and Heskey spun to hook home from six yards for his ninth goal of the season and histhird in six games.
Taylor was soon back in flying action after the break to block a fierce angled drive from Smicer, and it seemed only lack of concentration would harm Liverpool now.
That almost happened when Dudek nearly gave Fulham an equaliser, half hitting a clearance straight at Luis Boa Morte, who raced into the box only to be dispossessed by the excellent Djimi Traore.
Owen should have snatched a second, but after Smicer had got to the line and laid the ball back, the England striker scuffed the easiest of close range finishes.
Sixty seconds later he put all that right when Smicer's ball sent Owen scampering away - and he calmly drilled his shot past the exposed Taylor from the edge of the box.
Only then did Fulham become adventurous.
Dudek was forced into a fine block after Saha had raced from halfway, but the Polish goalkeeper could do nothing about a fierce drive by the same player which smashed against the bar with 10 minutes left.
But it was too little too late from Fulham, who will view the end of their campaign with jangling nerves while Liverpool turn their attention towards next Saturday's day of destiny - the Merseyside derby.