Pedro opened the scoring on nine minutes, latching on to a searching David Luiz pass before lobbing Martin Dubravka.
Ciaran Clark equalised five minutes before the break, powerfully heading Matt Ritchie's corner into the bottom left corner.
Pedro was denied a second goal two minutes after the restart before Willian restored Chelsea's lead with a curling effort from the edge of the penalty area.
Salomon Rondon came close to earning a point for the visitors late on, but headed Javier Manquillo's cross just wide of the target.
The win means Chelsea are within a point of third-placed Tottenham Hotspur, who face Manchester United on Sunday, and six clear of Arsenal, in fifth.
Newcastle are third from bottom with 18 points.
Chelsea: 19 Jan v Arsenal (A)
Newcastle: 19 Jan v Cardiff (H)