Eddie Howe's side were good value for their two-goal lead at the break, with a pair of smart finishes from the German frontman 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 - has cut their lead in half at the start of the second half.
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 home 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, as 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.
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.
**Newcastle United:** Aaron Ramsdale, Lewis Hall, Fabian Schär, Sandro Tonali, Anthony Gordon, Malick Thiaw, Jacob Murphy, Nick Woltemade, Bruno Guimarães, Jacob Ramsey, Lewis Miley
**Substitutes:** John Ruddy, Joelinton, Yoane Wissa, Harvey Barnes, Anthony Elanga, Joe Willock, Alex Murphy, Leo Shahar, Sean Neave