Lee Carsley's curling free-kick earned high-flying Everton a point in manager David Moyes' 100th Premiership game.
Craig Bellamy burst through to make it 1-0 before Jermaine Jenas' volley hit the bar and Alan Stubbs cleared Patrick Kluivert's effort off the line.
Stubbs and Tim Cahill went close before half-time and the chances continued to come thick and fast after the break.
After Carsley levelled, Bellamy hit the post, Marcus Bent missed a good chance and Shay Given denied Leon Osman.
Everton began in the bright manner that has helped them surpass all expectations this season and Bent's looping header from Tony Hibbert's cross drifted just wide of the far corner.
But it was all Newcastle for the next 15 minutes and they opened the scoring with a move that was devastating in its simplicity.
Shay Given's kick forward was flicked on by Lee Bowyer and, after a neat one-two between Bellamy and Kluivert, the Wales striker's searing pace took him clear to finish with aplomb.
Newcastle's pace and precise passing was causing all sorts of problems for the visitors and Jenas was twice unlucky not to add a second goal.
He almost finished off a superb move he had started from the halfway line when he collected a pass from the impressive Kluivert before Martyn denied him with an excellent save.
And he was even closer when his acrobatic volley canoned off the woodwork after the ball had bobbled about in the Everton penalty area.
There was another close call for the Toffees when, after they had failed to clear Bellamy's cross, Kluivert's shot was heading into Martyn's right corner before Stubbs cleared it off the line.
But Everton finally came into the game towards the end of the first half and nearly snatched an equaliser they scarcely deserved when Thomas Gravesen's free-kick fell to Stubbs at the other end but this time his shot was parried by Given.
A succession of corners followed and Stubbs' goalbound header was accidentally blocked by Cahill, whose back-heeled effort was inches wide.
Moyes sent his side out early to warm up for the second half and, no doubt spurred on by some choice words from him, resumed the game with plenty of purpose.
Cahill had a decent shout for a penalty when young right-back Steven Taylor pushed him in the back but the midfielder was the only one to protest.
Sparked into life, Newcastle tried to regain control of the game and Kieron Dyer was the next to benefit from Kluivert's vision when he ran on to his through-ball but, after rounding Martyn, he failed to squeeze in from a difficult angle.
Kluivert was then presented with a half-chance to net a goal he richly deserved when Bellamy played him in but his shot was high and wide.
But Carsley stunned the home crowd when he curled a sublime 30-yard free-kick
into the top corner, with Given barely moving to his left.
An already-entertaining game began opening up further and Bellamy joined Jenas in hitting the woodwork when his raking drive crashed off the post with Martyn well-beaten.
However, Everton should have completed a remarkable turnaround when Gravesen's delightful touch put Bent clear but he could not find the net after taking the ball wide of Given.
The pace did not abate in the closing minutes and it was Dyer's turn to feel aggrieved when he collided with Kevin Kilbane but referee Neale Barry appeared correct to ignore cries for a penalty.
Fittingly, the game ended with both teams going close to winning it.
Bellamy should really have made the points safe when Kluivert crossed from the left and the ball fell to him in acres of space.
But Alessandro Pistone blocked his fierce drive and, almost immediately, Osman's 20-yard effort was tipped around the post by Given.
Newcastle: Given, Taylor, Bramble, Hughes, Bernard, Jenas,
Dyer, Bowyer (Ameobi 81), Robert, Bellamy, Kluivert. Subs Not Used: Milner, Ambrose, Brittain, Harper.
Goals: Bellamy 5.
Everton: Martyn, Hibbert, Stubbs, Weir, Pistone,
Cahill (Watson 86), Osman, Gravesen (Yobo 90), Carsley,
Kilbane, Bent (Ferguson 88). Subs Not Used: McFadden, Wright.
Booked: Cahill, Hibbert, Bent.
Goals: Carsley 56.
Ref: N Barry (N Lincolnshire).