Dirk Kuyt's injury-time penalty gave Liverpool a crucial Merseyside derby win against nine-man Everton.
Liverpool celebrate Dirk Kuyt's first penalty at Everton
Sami Hyypia sliced into his own goal after 37 minutes to give Everton the lead at the interval.
But Kuyt scored from the spot after 54 minutes when Tony Hibbert was sent off for hauling down Steven Gerrard as he raced clear on goal.
And Kuyt struck again in time added on, with Phil Neville also sent off for handling Lucas' goal-bound shot.
Everton were then furious with referee Mark Clattenburg, who ignored strong claims for a spot-kick in the dying seconds when Jamie Carragher clearly dragged down Joleon Lescott.
Liverpool were without groin-injury victim Fernando Torres, while Everton resisted the temptation to recall long-term absentees Tim Cahill, Thomas Gravesen and James Vaughan.
Benitez's side started better and should have taken the lead in the fourth minute when Andriy Voronin shot straight at Everton keeper Tim Howard after Hibbert's hesitation let in Yossi Benayoun.
Everton, however, quickly came to terms with Liverpool's system and Lescott was a constant threat down the left flank.
John Arne Riise had a long-range free-kick deflected just wide, but Liverpool were in danger of losing their early momentum.
Victor Anichebe had two headers off target before Everton took the lead with a freak goal eight minutes before the interval.
Alan Stubbs retrieved a corner and crossed into the area, where Hyypia inexplicably lashed the ball past his own keeper Pepe Reina with his left foot.
Liverpool needed a break to get back into the game and they got it via a penalty and a red card for Everton's Hibbert.
Gerrard led a Liverpool break with a surge into the area where he was hauled down by Hibbert.
Referee Clattenburg pointed the spot and sent Hibbert off before Kuyt sent Howard the wrong way from the spot for his first league goal of the season.
Liverpool then attempted to make their most of their numerical advantage, with Riise shooting wildly over when unmarked and then Voronin having a shot blocked by Howard from close range.
Yakubu, who had been having a quiet afternoon, almost restored Everton's lead with a stunning 30-yard drive that whistled inched wide with Reina beaten.
Benitez then sprung a surprise with 20 minutes left, sending on Brazilian youngster Lucas for Gerrard - who looked stunned to be called off.
As the game went into injury-time, Liverpool grabbed a lifeline when Neville dived to palm away Lucas' shot.
Kuyt scored, but Everton were enraged when Carragher fouled Lescott in front of referee Clattenburg, who waved away their appeals.
Everton boss David Moyes:
"Decisions happen, that's football. But in the last seconds there's the chance for it to be corrected and it would've been a result we deserved.
"We deserved that penalty and if the other penalties were more blatant than that, then I am in the wrong game.
"I seem to see football differently. If the ref doesn't see that you ask why."
Liverpool boss Rafael Benitez:
"People talk about a penalty they could have had. But last season we lost here 3-0, two of their goals were fouls and nobody complained then.
"I always feel that in England, players should not be rewarded with penalties for diving.
"I felt both penalty decisions were right. And I also agree with the yellow card for Kuyt and not a red."
Everton: Howard, Hibbert, Yobo, Stubbs, Lescott, Arteta, Jagielka, Neville, Osman, Yakubu (McFadden 77), Anichebe (Baines 84).
Subs Not Used: Wessels, Pienaar, Carsley.
Sent Off: Hibbert (53), Neville (90).
Goals: Hyypia 38 og.
Liverpool: Reina, Finnan, Carragher, Hyypia, Riise, Gerrard (Lucas 71), Mascherano, Sissoko (Pennant 88), Benayoun (Babel 68), Voronin, Kuyt.
Subs Not Used: Itandje, Crouch.
Booked: Kuyt, Carragher.
Goals: Kuyt 54 pen, 90 pen.
Ref: Mark Clattenburg (Tyne & Wear).