Liverpool and Everton played out a pulsating deadlock at Anfield.
Everton's veteran goalkeeper Nigel Martyn was the hero with a string of outstanding saves to earn a point.
He denied Liverpool captain Steven Gerrard twice, tipping one drive on to a post, and also saving well from Dietmar Hamann and Jamie Carragher.
Everton also had chances, with Duncan Ferguson heading wide of an open goal and Liverpool goalkeeper Jerzy Dudek making two fine stops from Alan Stubbs.
Everton opted for an attacking formation, with Wayne Rooney starting alongside Duncan Ferguson and Tomasz Radzinski.
And the positive intent of both sides showed in a sparking first 45 minutes highlighted by brilliant displays from Martyn and Liverpool counterpart Jerzy Dudek.
In the opening minutes Dudek dived bravely at Ferguson's feet, then Martyn showed brilliant agility to turn Hamann's drive over the top.
Gerrard was driving his side forward, and he was the player who suffered most at the hands of the veteran Martyn.
Rooney challenges Carragher
He raced on to Michael Owen's pass but was denied by a fine Martyn save, and was cursing the 37-year-old again eight minutes before the interval when he turned a shot on to a post.
But Everton were more than matching Liverpool, and they were furious when Sami Hyypia appeared to impede Radzinski but referee Steve Bennett waved away their appeals.
Then as half-time approached, Ferguson missed a simple header from close range following Rooney's pinpoint cross.
Dudek emulated the feats of Martyn with a stunning save from Alan Stubbs' header as Everton pressed for the opener.
Everton started the second half on the attack and Rooney shot just over the bar after working his way past three defenders.
But Gerrard was not to be overshadowed by his close friend and England team-mate, and he was then narrowly off target.
Liverpool's in-form midfield man Bruno Cheyrou, with four goals in five games, was off target after 54 minutes when he flicked Anthony Le Tallec's cross wide.
Le Tallec then almost broke the deadlock, only to see his effort scrambled off the line by Ferguson.
Dudek still had to turn aside Stubb's fiercely-struck free-kick from 30 yards as Everton still posed a threat.
Everton were under the cosh, and as time ran out Moyes replaced Rooney with the more defensive-minded Steve Watson after bringing on Francis Jeffers for Tomasz Radzinski.
Liverpool continued to press, but Everton were resolute to the end and will be delighted with a point.#
Liverpool: Dudek, Finnan, Henchoz, Hyypia, Carragher, Hamann,
Gerrard, Le Tallec, Cheyrou, Kewell, Owen.
Subs Not Used: Luzi Bernardi, Murphy, Riise, Traore, Biscan.
Everton: Martyn, Hibbert, Stubbs, Pistone, Naysmith,
Rooney (Watson 77), Gravesen, Nyarko (Carsley 58), Kilbane,
Ferguson, Radzinski (Jeffers 73).
Subs Not Used: Simonsen, Clarke.
Referee: S Bennett (Kent).