A Stoke defence without three first-choice players took just three minutes to concede, as Antonio Rudiger headed in Willian's free-kick.
Danny Drinkwater then scored his first Chelsea goal, a volley from 25 yards, before Pedro made it 3-0 on 23 minutes from Willian's second assist.
Stoke thought they had pulled one back just before half-time but Mame Biram Diouf's effort was ruled out for handball.
Willian won and converted a penalty after the break and, on 88 minutes, Davide Zappacosta smashed in his first PL goal.
Chelsea have won seven in a row at home and go above Manchester United, who drew with Southampton. Stoke are 15th.
Chelsea: 3 Jan v Arsenal (A)
Stoke: 1 Jan v Newcastle (H)