The 37-year-old Drogba was allowed to make the unusual, lengthy mid-game farewell to Chelsea fans after being theatrically substituted around 30 minutes into the game.
Drogba was carried to the touchline by his teammates before waving goodbye to each corner of Stamford Bridge.
There was no final goal for Drogba, with his replacement, Diego Costa, instead quickly scoring from the penalty spot to cancel out Steven Fletcher's Sunderland opener.
Loic Remy then scored twice for the champions in the second half.
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