The veteran rocker performed with the six-piece band on the closing night of week one of the event in Indio, California.
Debbie, 68, sang with the band's Régine Chassagne on her 1978 hit 'Heart Of Glass', before staying to perform their song 'Sprawl II (Mountains Beyond Mountains)', after which frontman Win Butler shouted, ''Debbie f****ng Harry'' to the crowd.
The band were introduced by a man wearing a suit made of broken mirrors and opened up their set with 'Reflektor'.
Win said: ''Alright guys, we're gonna give you every ounce of what we've got if you give it back to us (sic).''
The singer, who is married to Régine, also slammed Coachella's ''fake VIP room b******t,'' telling the audience the exclusive area in the festival grounds ''super sucks'' and not to worry about not getting access.
Fans sat in the non-VIP beer garden next to the area cheered and Win also quipped: ''Shout-out to all the bands still playing actual instruments at this festival.''
The band - also made up of Richard Reed Parry, William Butler, Jeremy Gara, Tim Kingsbury - also handled a power cut well, telling fans to ''keep singing'' before marching into the crowd with a megaphone.