Steely Dan - Aja and The Royal Scam (on different nights -- it was a 3-night run, with the 3rd night for "Internet Requests"; I only got tix for the 2 "album-plus" shows). Before they started the album sets, a woman with a 70s afro in a 70s outfit came out on stage and put a record down on a turntable at the side of the stage. She came out and flipped the record halfway through.
The Cult - Love.
Judas Priest - British Steel.
Exodus - Bonded by Blood.
Testament - The Legacy and about 90% of The New Order (same show, but songs not all in exact album sequence)
Almost but not quite: Queensryche, almost all of Operation: Mindcrime (except "Suite: Sister Mary") in 1989.
And this probably doesn't count, but I saw Maiden play the first three sides of Live After Death in 1985, before the album came out.