Eddie Howe's side were good value for their lead at the break, with a pair of smart finishes from Nick Woltemade just reward for a front-foot, aggressive display in the opening 45 minutes on Tyneside.
But Reece James' free kick - curled into the bottom corner beyond Aaron Ramsdale - cut their advantage in half at the start of the second half, before João Pedro levelled the scores on 75 minutes to earn the visitors a share of the spoils.
Barely three minutes in, the Magpies took the lead. Jacob Murphy's cross from the right found Anthony Gordon, whose close-range effort was somehow kept out by a sprawling Robert Sánchez, with the rebound falling kindly for Woltemade to hammer into the roof of the net.
Gordon almost doubled United's lead on seven minutes, forcing Sánchez into a fine reflex save to turn his shot over the bar, with Sandro Tonali then almost catching the Blues stopper out direct from a corner as Howe's men began brightly.
And they were rewarded for their dominance with a deserved second goal midway through the half. Gordon's inswinging cross was perfect for Woltemade, who delicately diverted the ball into the bottom right-hand corner to double the Magpies' advantage, with the German international's second of the afternoon allowed to stand after a protracted VAR check.
It could have got even better for the hosts before the interval when Fabian Schär connectly sweetly with Lewis Hall's free kick, but the Swiss defender's back-post volley was well held by Sánchez.
Pedro Neto did have the ball in the net for Chelsea, turning home Alejandro Garnacho's centre from the left with 41 minutes on the clock, but the goal was swiftly and correctly chalked off after he used his hand to divert it past Aaron Ramsdale.
And there was still time for Woltemade to go close to his hat-trick when he turned a Gordon cross just wide at full stretch as the Magpies continued to apply pressure in the final moments of an impressive first half showing.
But James' 25-yard free kick - awarded following Jacob Ramsey's foul on Cole Palmer - reduced the deficit just three minutes after the restart as Enzo Maresca's visitors sought a foothold in the contest, and the goal did alter the flow of the game.
A Trevoh Chalobah challenge on Gordon could arguably have led to a penalty shortly after, though referee Andy Madley was unmoved, and as the game opened up even further, the Blues began to probe for a leveller with James seeing a low strike blocked by Schär. Neto then led a counter-attack which culminated in the Portuguese winger forcing Ramsdale to parry his left-footed effort.
The United backline were being tested far more than in the first period and Schär did well to get in front of substitute Enzo Fernández following another quick breakaway, but with 25 minutes left the equaliser arrived. Sánchez collected a Gordon cross and looked to set Pedro away quickly, with Malick Thiaw's unfortunate slip presenting the Brazilian with an opportunity he didn't pass up, rolling under Ramsdale to make it 2-2.
Howe responded with a triple change, introducing a new front three in the shape of Anthony Elanga, Yoane Wissa and Harvey Barnes, and the latter was played in by Wissa with just over ten minutes remaining only for James to recover well and prevent the shot.
In an end-to-end finish to an absorbing second half, Moisés Caicedo whipped a shot just past the upright and Garnacho cut inside and took aim, with Ramsdale doing well to keep it out at his near post. Barnes had another opening after captain Bruno Guimarães led an attack and picked him out brilliantly in the box, but the former Leicester winger's first-time attempt flew off target.
In the final minute of the 90, Elanga was freed by a long throw from Ramsdale and raced through on goal, but couldn't quite find the far corner with a curling shot. A VAR check in added time led to nothing following Chalobah's challenge on Barnes and only added to a frustrating afternoon for those in black and white, with Chalobah having appeared to have hauled down the wideman as he looked to latch on to a ball over the top.
It was a fittingly breathless end to a fine game - but one which United may feel they should have taken more than just a point from.
Newcastle United: Aaron Ramsdale, Lewis Hall, Fabian Schär, Sandro Tonali, Anthony Gordon (Harvey Barnes 72), Malick Thiaw, Jacob Murphy (Anthony Elanga 72), Nick Woltemade (Yoane Wissa 72), Bruno Guimarães, Jacob Ramsey (Joe Willock 90), Lewis Miley
Subs not used: John Ruddy, Joelinton, Alex Murphy, Leo Shahar, Sean Neave
