Everton delivered an outstanding defensive display to earn a point against Liverpool at Anfield.
Everton's Leon Osman battles with Liverpool defender Steve Finnan
Liverpool dominated possession, with Craig Bellamy having an early goal ruled out for offside and Tim Howard saving well from Peter Crouch.
But Everton had the best chance of the game after 59 minutes when Andrew Johnson shot straight at Pepe Reina as he looked certain to score.
Crouch also wastefully shot straight at Howard as time ran out for Liverpool.
Everton unveiled a surprise in their team selection, with Johnson declaring himself fit from the ankle injury sustained at Wigan a fortnight ago that originally threatened to rule him out for the rest of the season.
Tony Hibbert, also playing his first Premiership game since October after a groin problem, had the first clear chance after only five minutes.
He stole in at the edge of the area, but his crisp shot was straight at Reina.
Crouch brought a fine block from Everton keeper Howard three minutes later when the Liverpool striker fired in a shot from only eight yards.
Liverpool thought they had taken the lead after nine minutes when Bellamy rounded off an exchange of passes with Dirk Kuyt before beating Howard - but he had strayed offside in the build up.
Johnson looked lively, despite playing under an injury cloud, and he set up a chance for Leon Osman, who could only direct a header towards Reina.
Everton's hard-work and organisation had kept Liverpool at arm's length, but Xabi Alonso almost broke the deadlock on the half-hour with a dipping 25-yard shot that was only inches over the top.
Liverpool had penalty appeals rejected by referee Alan Wiley after 50 minutes when Phil Neville blocked Jamie Carragher's goal-bound shot following a corner - but replays suggested that ball had struck the Everton captain's shoulder.
Everton had the best chance of the game after 59 minutes when the excellent Joleon Lescott broke up a Liverpool attack and helped Johnson break clear into the area, but Reina made a crucial stop with his legs from 12 yards as a goal looked certain.
Gerrard was then inches away with a free-kick as Liverpool finally tested the resilience of Everton's rearguard.
Liverpool made a change with six miniutes left, sending on Robbie Fowler for Bellamy - but the veteran striker made no impact.
Crouch then had a glorious chance when the ball fell to him only eight yards out, but he could only half-hit a shot at Howard.
Liverpool manager Rafael Benitez:
"I'm really disappointed. One team wanted to win and one didn't want to lose but we tried to keep going forward and creating chances.
"When you play against eight players behind the ball, narrow and deep, you cannot create many clear chances.
"You just keep trying. You cannot say anything about this."
Everton boss David Moyes:
"We've played them twice now and not conceded, so credit to the defenders.
"We've seen what Chelsea had to put up with when they came here, Liverpool are a really good side.
"Stubbs and Neville are very popular lads in the dressing room and they both put in excellent performances today. Stubbs' experience shone through."
Liverpool: Reina, Finnan, Carragher, Agger, Riise, Pennant, Alonso, Gerrard, Bellamy (Fowler 85), Kuyt, Crouch.
Subs Not Used: Dudek, Hyypia, Gonzalez, Zenden.
Everton: Howard, Hibbert, Yobo, Stubbs, Lescott, Carsley, Neville, Cahill, Arteta, Osman, Johnson (Anichebe 80).
Subs Not Used: Wright, Naysmith, Beattie, Fernandes.
Booked: Osman, Neville, Arteta.
Ref: A Wiley (Staffordshire).