It looked as though the Reds were going to pay for missed chances until the Israel international midfielder blasted a right-footed shot past Fulham goalkeeper Mark Schwarzer.
The win put Rafael Benitez's men two points clear at the top of the table - although second-placed Manchester United have two games in hand.
Elsewhere returning Newcastle hero Alan Shearer could only look on from the sidelines as his side lost 2-0 at home to Chelsea.
Former captain Shearer received a rapturous reception as he made his debut in the dug-out after stepping in for the last eight games of the season in a bid to save the beleaguered club from Premier League relegation.
With his side third from bottom and three points from safety at the beginning of the day, Shearer had vowed to go for the win at St James' Park but despite their positive play, his side ended the day empty-handed.
Some terrible defending by Fabricio Coloccini gifted Nicolas Anelka a chance and when the Frenchman's shot hit the bar, Frank Lampard was on hand to convert the rebound.
It was quickly 2-0 when Florent Malouda capitalised on more slack defending to fire under Steve Harper and put the game beyond the hosts.
Newcastle should have pulled one back when Michael Owen's deflected shot appeared to go over the line before Ashley Cole cleared, but the goal was not given.
Returning duo Emmanuel Adebayor and Cesc Fabregas combined twice to give Arsenal a 2-0 win against Manchester City at Eastlands.
Captain Fabregas, back from a long injury lay-off, placed a delicate free-kick onto Adebayor's head for the Togo striker to nod home unmarked after eight minutes.
Fabregas' undoubted influence was in evidence again after the break when he played Adebayor in and Richard Dunne's failure to clear allowed the striker to double the lead in the 49th minute.
Stoke gave their survival bid a massive boost with a 2-0 win over Tony Mowbray's hapless West Brom at the Hawthorns.
Ricardo Fuller put Stoke ahead in the second minute after some poor defending and goalkeeping saw his speculative shot squirm under Scott Carson.
Albion started the second half as badly as the first and this time it was James Beattie who rifled past Carson, hitting the ball sweetly just four minutes after the break.
Middlesbrough lost 4-1 at Bolton to leave their survival hopes looking bleak.
Kevin Davies had given Bolton an eighth-minute lead only for Gary O'Neil to score a deserved equaliser seven minutes before the break. However, with half-time approaching, defender Gary Cahill was on the spot to restore the Trotters' lead.
Then Matthew Taylor's 78th-minute crossed free-kick somehow drifted past Brad Jones before Ricardo Gardner added a fourth to compound Boro's misery.
West Ham enjoyed a 2-0 win at home to Sunderland after goals by two young prospects.
After a largely tepid 42 minutes, West Ham goalkeeper Robert Green threw the ball out to initiate a superb counter-attack which finished with Luis Boa Morte feeding Junior Stanislas for the youngster to tap home.
In the second half James Tomkins' 53rd-minute header from Mark Noble's corner made sure of the points.
Hull and Portsmouth cancelled each other out at the KC Stadium despite both pushing hard for an unlikely winner.
While Hull opted to bombard the flanks in search of a goal, Portsmouth tried to play down the middle for much of the encounter but both sides were unable to produce a winner.
Pompey had to play for the last 10 minutes with 10 men after Glen Johnson was sent off for two bookable offences but the Tigers could not take advantage.
In the lunchtime Premier League kick-off, Blackburn substitute Andre Ooijer scored a dramatic late winner against Tottenham to secure a 2-1 victory and ease his side's fears of relegation.
Tottenham had opened the scoring through a Robbie Keane penalty but then saw Wilson Palacios sent off before Benni McCarthy equalised.