After withstanding the Blues' dominant attacking pressure for over an hour, Graeme Jones' side fell behind through Reece James' emphatic strike before the right-back's drilled finish doubled the visitors' advantage.
Jorginho's penalty extended Chelsea's lead further in the closing stages as the Magpies' winless Premier League run extended to ten matches.
Jones named an unchanged starting XI from the side which claimed a 1-1 draw at Crystal Palace last weekend and faced a Chelsea side who had netted 16 goals in their previous five competitive matches, including seven against Norwich City in their recent league fixture.
The hosts created a rare glimpse in front of goal as Allan Saint-Maximin and Ryan Fraser combined neatly before the latter's teasing pass across the face of goal flashed narrowly past the penalty area.
Wilson, who had netted four goals in five league fixtures, then nodded a header wide of Édouard Mendy's goal following Matt Ritchie's in-swinging free-kick from the left wing.
Thomas Tuchel's side looked to have taken the lead before the half-hour mark through Hakim Ziyech as the Moroccan controlled Jorginho's dangerous pass before curling the ball beyond Darlow but, after straying into an offside position, the goal was disallowed.
The attacking midfielder went close to breaking the deadlock shortly after as James' low cross from the right flank was directed into the 28-year-old's path but his first-time effort sailed over the crossbar.
With the half-time whistle approaching, United captain Jamaal Lascelles created a half chance after connecting with Clark's hooked cross from the left flank but the defender's headed attempt failed to trouble Mendy.
In the second-half, Newcastle were fortunate to remain on level terms as Ziyech's strike from the edge of the box deflected off Lascelles, deceiving Darlow, before bouncing off the left-hand post.
However, in the 65th minute, Chelsea broke the deadlock through James' impressive finish. After Ritchie could only flick Callum Hudson-Odoi's inviting cross towards James at the back post, the right-back controlled the ball before drilling his effort into the top left-hand corner.
In the 77th minute, United were dealt another difficult blow as James notched his brace. After the 21-year-old teed up Ruben Loftus-Cheek inside the penalty area, the midfielder's strike was blocked by Clark before the ball fell kindly into the full-back's path, who drilled the ball home.
Four minutes later, Newcastle fell further behind as Jorginho converted from the penalty spot. After Kai Havertz was brought down inside the box by Darlow, following Loftus-Cheek's forward pass, the Italian midfielder made no mistake from 12 yards, sending Darlow the wrong way.
Newcastle United: Karl Darlow, Javier Manquillo, Emil Krafth, Jamaal Lascelles (c), Ciaran Clark, Matt Ritchie, Isaac Hayden (Miguel Almirón 66), Sean Longstaff (Jonjo Shelvey 81), Ryan Fraser (Joe Willock 66), Allan Saint-Maximin, Callum Wilson.
Subs not used: Martin Dúbravka, Jacob Murphy, Fabian Schär, Jamal Lewis, Joelinton, Dwight Gayle.
