A penalty from Eden Hazard and a header from Joselu - both netted in controversial circumstances - saw the teams remain on level terms heading into the final stages, but an own goal from DeAndre Yedlin gifted Chelsea all three points.
The Blues have now won three successive matches under new head coach Maurizio Sarri - and the triumph in the North-East ends a run of five games without a win at the home of the Magpies - while Newcastle remain without a win after a second consecutive home defeat.
Antonio Rudiger sent a speculative effort wide at the other end, but the first real opportunity for the visitors did not materialise until the 25th minute when Hazard fired wide of the far post from 20 yards.
Newcastle improved as the first half progressed and Salomon Rondon should have done better with a header from 12 yards out, but Chelsea were soon back onto the offensive with Pedro curling over the far top corner from the same distance.
The Spaniard was also denied by Martin Dubravka a minute later, with the Czech stopper anticipating Pedro's low shot towards the bottom corner, but Newcastle were able to remain on level terms heading into the break despite gifting Chelsea the majority of the ball.
The same pattern of play continued after the restart, and Cesar Azpilicueta should have done better after good work from Hazard and Pedro but fired his 20-yard shot too close to Dubravka.
The Blues continued to struggle as the game entered the final 15 minutes - although Rudiger did strike the crossbar with an audacious attempt from distance - but Sarri's men were given their opportunity to take the lead when the referee gave a contentious penalty decision in their favour.
Fabian Schar appeared to win the ball from Marcos Alonso but the referee adjudged the challenge to be a foul, and Hazard made no mistake from the spot with his effort being swept into the left corner.
Newcastle felt hard done by, but Chelsea were justified in experiencing the same emotions seven minutes later as the home side pushed forward and found an equaliser.
Yedlin appeared to elbow Giroud on the right flank, but no foul was given and the United States international proceeded to cross the ball towards the near post where Joselu powered a header inside of the near post.
However, Chelsea were soon back in front as Yedlin went from hero to villain. Alonso's volley from inside the penalty area was heading wide and may have been turned in by Ross Barkley at the back post, but Yedlin stuck a foot out to divert the ball into the corner.
Newcastle attempted to salvage a point that they barely deserved based on their ambition earlier in the contest, but Chelsea held on to move level on points with Liverpool and Watford.
NEWCASTLE UNITED (5-4-1): Dubravka; Yedlin, Schar (Muto 79'), Fernandez, Clark, Dummett; Ritchie, Ki, Diame, Murphy (Perez 73'); Rondon (Joselu 62')
CHELSEA (4-3-3): Kepa; Azpilicueta, Rudiger, Luiz, Alonso; Jorginho, Kovacic (Barkley 79'), Kante; Pedro (Willian 69'), Hazard, Morata (Giroud 65')