After fifth-placed Arsenal's loss earlier in the day, Chelsea are now six points clear of their London rivals in the race for Champions League qualification.
Chelsea immediately took control of the majority of the possession and opened the scoring in the ninth minute. David Luiz played a sumptuous through-ball for Pedro, who brought the ball down excellently before lofting it over the out-coming Martin Dubravka.
Luiz had an opportunity to double the lead in the 24th minute but powered his header over the bar from Willian's out-swinging free-kick.
Newcastle, however, were growing in to the game and gaining more possession of the ball and Ayoze Peres should have done better in the 35th minute when through on goal but could only slash his effort horribly wide.
Five minutes later though, the Magpies would be rewarded for their endeavour. After Matt Ritchie's corner was headed back out, Ritchie delivered another curler in to the box for Ciaran Clark to head home a superb finish.
Pedro had a chance to grab his brace and restore Chelsea's lead barely a minute in to the second half, but Dubravka pulled off a brilliant save to deny the Spaniard.
Maurizio Sarri's side would have their second and it came in the 57th minute courtesy of sheer individual brilliance from Willian, who curled his effort in to the far corner from a near-impossible angle after a mazy run from Eden Hazard.
Luiz played another excellent through ball in the 64th minute with the recipient this time Willian, who only had the keeper to beat but lobbed his effort just wide of the post.
The Magpies would try as they might to break down the stubborn Chelsea rearguard, but it would to be no avail as the Blues held on for a crucial win.