The Brazilian forward, linked with a move to Barcelona before the transfer window closes, curled the ball past Martin Dubravka shortly before the hour to move his side six points in front of fifth-placed Arsenal.
Newcastle have now lost 10 in a row away to the division's established top six, but they put up a good fight in West London, levelling up through Ciaran Clark after Pedro opened the scoring, only for Willian to win the match for Chelsea.
After failing to score in their last two home league matches - a 1-0 defeat to Leicester City and 0-0 draw with Southampton either side of Christmas - it took the Blues just nine minutes to edge in front here.
Chelsea cruised through the opening half-hour of the match, with Pedro coming close to a second goal from his 25-yard drive, which Dubravka was equal to, and Luiz's header took a small touch on its way marginally wide of the target.
Maurizio Sarri's men would pay for their failure to create anything clear cut, though, as Newcastle soon started to grow into the match.
Florian Lejeune fired a long-range volley through a sea of bodies for Kepa Arrizabalaga to make his first save, while Ayoze Perez sliced wide of the target after latching on to Salomon Rondon's flicked pass.
The leveller then arrived five minutes before half time, as Clark made amends for being caught out for Chelsea's opener by getting in front of Luiz and powering home a corner.
Willian should have put Chelsea back in front before the interval, failing to find a way through when one on one with Dubravka, who kept out a couple of Pedro shots in the opening 13 minutes of the second half.
A minute after that second Pedro miss, Willian edged the Blues back in front with a delightful curler into the far corner after cutting inside on his right foot.
Willian was unable to double his tally when, like Pedro before him, he was played through with a simple lofted pass, with Dubravka this time getting a touch to the attempted lob.
Callum Hudson-Odoi was brought off the bench for the final 10 minutes of the match in place of Pedro, having been left out of the starting lineup in one of three changes, but the Bayern Munich target could not help to kill off the match.
Newcastle, now with just one win in nine Premier League outings, enjoyed their fair share of possession in the remainder of the match, but Rondon's wayward header at the back post three minutes from time was the best they could offer.
This loss in the capital, combined with results elsewhere on Saturday, means that United are now in the relegation zone ahead of next week's huge showdown with fellow strugglers Cardiff City.
CHELSEA (4-3-3): Kepa; Azpilicueta, Rudiger, Luiz, Alonso; Kante, Jorginho, Kovacic; Willian, Hazard (Giroud 87'), Pedro (Hudson-Odoi 81')
NEWCASTLE UNITED (3-5-1-1): Dubravka; Yedlin (Manquillo 82'), Lascelles, Lejeune; Clark, Hayden, Longstaff, Atsu, Ritchie; Perez (Murphy 82'); Rondon