Chelsea put aside the club’s off-the-pitch issues to cement their position in third place.
Early goals from Trevoh Chalobah and Mason Mount put the Blues in control against struggling Norwich, who rallied in the second half and pulled a goal back through Teemu Pukki’s penalty after Chalobah’s handball.
Kai Havertz sealed the win with a last-minute strike.
Chalobah opened the scoring with a glancing header from Mount’s fourth-minute corner.
And Mount doubled the lead with a lovely finish 10 minutes later.
Havertz sped past Christoph Zimmermann and squared the ball to Mount, who cleverly evaded Ozan Kabak and fired into the top corner of the net.
Norwich were given hope by Pukki’s spot-kick and Chelsea had to withstand some pressure in the later stages.
Romelu Lukaku, on as a substitute, missed a chance to make it 3-1 before Havertz did so with an emphatic finish after being teed up by N’Golo Kante.
Chelsea: Mendy, Chalobah, Silva, Christensen, Azpilicueta (Loftus-Cheek 45), Kovacic (Kante 85), Jorginho, Saul, Mount, Havertz, Werner (Lukaku 85).
Subs not used: Kepa, Rudiger, Ziyech, Kenedy, Sarr, Vale.