Benayoun, who had entered the field in the 76th minute, scored in extra time (90 +2), when the Liverpool attack constantly but could not break the tie with no goals against a team that was ninth in the table.
But in the end, both the Israeli leaders to put the 'Reds', two points ahead of Manchester United, who recovered the lead on Sunday if they win in their field of Aston Villa at Old Trafford.
In addition, Alex Ferguson's team has the advantage of having one less game, which has to compete against Portsmouth at home.
Liverpool, despite the late goal, in marking the eighth time this season in injury time, victory was won at Craven Cottage, throwing four balls to by both clubs.
A header from Martin Skrtel (10), a semivolea from Xabi Alonso (33) and a plate testarazo Andrea Dossena (37) hit the crossbar, while a cross-shot Fernando Torres struck in one of the poles (35) .
When Liverpool launched a shot from the three sticks, goalkeeper Mark Schwarzer was vigilant, and once Torres (23).
In the second period, Liverpool were less convincing before awakening at the end of the match, with Ryan Babel missed opportunity in a backlash (71), Torres (73) and Steven Gerrard (82).
When everything seemed lost, Benayoun received a ball to the left of the goal of Schwarzer and marked with both a cross-shot (90 +2).
"Being honest, I thought that it would not be our day. Yossi blow came this great. Now, we expect for (Aston) Villa. We will continue to remind the United winning that we are there," said Gerrard.
For their part, Chelsea and Arsenal, respectively, were imposed in the area of Newcastle (2-0) and Manchester City (2-0).
The 'Blues' still in third place, three points from Liverpool and a temporary Manchester United after their victory over Newcastle, where the return as coach of the team Alan Shearer was not accompanied by a miracle.
The first came after both of Chelsea an error Fabrizio Coloccini Argentine defense, which allowed the French Nicolas Anelka intercept the ball. The shot hit her in the French club and Frank Lampard took the rebound and scored in the 56th minute.
In a funeral at St. James' Park, the French Florent Malouda, Lampard served, succeeded after his first in five months (65) and put more concern in Newcastle, which is in the area of descent (18 degrees), with three points less than his enemy, Sunderland defeated West Ham (2-0).
Arsenal chained his 17th match without defeat in league with the return of two injured, the Spanish midfielder Cesc Fabregas and Togo striker Emmanuel Adebayor.
And with Arsenal is another thing, since the Spanish took the two crucial passes to African player who scored the two so (8, 49) in an easy victory at Manchester City (2-0).
For his part, West Bromwich colista seems closer than ever to fall from second division following their defeat against Stoke City (2-0), another newly promoted.
Goleado in Bolton (4-1), Middlesbrough, does not seem to be much better, with five goals last disadvantage to Sunderland.