Chelsea made it three consecutive league wins but had to do it the hard way with Marcos Alonso's second-half strike proving the difference as Newcastle United suffered a 1-0 loss.
Newcastle were brimming with confidence after their 1-0 win over Manchester United last time out while Chelsea were looking to build on their two-game winning run. The Blues got their first chance in the 15th minute when Dubravka rushed off his line to clear the ball, but his clearance hit Abraham and looped out of target.
Ross Barkley was taken off in the 43rd minute with a suspected thigh injury and was replaced by Mateo Kovacic as Chelsea went into the half time break locked at 0-0 with Newcastle.
Chelsea entered the closing half with much impetus and found the crossbar in the 56th minute when Willian delivered a corner that was headed towards goal by Tammy Abraham but he was denied the game's opener by the crossbar.
Frank Lampard's men finally got the opener in the 73rd minute when Hudson-Odoi slid a composed pass into the path of Alonso after Pulisic broke into the box as the former Sunderland defender let the ball run across his body before drilling in a first-time shot into the bottom corner.
Chelsea held on for the win and will next face Ajax in a UEFA Champions League clash on Wednesday 23rd October as Newcastle United will look to pick themselves up against Wolverhampton Wanderers on Sunday 27th October.
Match Statistics: Chelsea 1-0 Newcastle United
Chelsea: Arrizabalaga, Azpilicueta, Zouma, Tomori, Alonso, Barkley, Jorginho, Willian, Mount, Hudson-Odoi, Abraham.
Subs: Caballero, Kovacic, Giroud, Pulisic, Batshuayi, James, Guehi.
Newcastle: Dubravka, Yedlin, Schar, Lascelles, Clark, Willems, Almiron, Matthew Longstaff, Sean Longstaff, Saint-Maximin, Joelinton.
Subs: Dummett, Carroll, Shelvey, Gayle, Krafth, Darlow, Atsu.