Though not a literary example, The Big Easy.
Nite Owl in Watchmen. Rorschach disagrees.
Darn it. I was going to post that one.
Actually, that was Ten Days’ Wonder. And don’t forget, Ellery had the real killer commit suicide rather than drag everything out into the open again! Although, in the title you erroneously used, he DID end up hiding the truth of the crime, because it was an accident, and revealing it would’ve shattered the “killer,” but there you are. 
In another great (but little-seen) Gene Hackman movie, Night Moves, the detective
about midway through finds that everything he thought was true about the case is wrong, and he’s been used as a pawn. It’s too late to straighten things out, but he tries, even at the risk of his fragile reconciliation with his estranged wife. There’s no happy ending, but at least you do finally get a complete picture of what was going on – if you look carefully to see who’s flying the plane at the end.
Angel Heart
The detective discovers that his client is Lucifer, and that the detective is both the missing person he was hired to find, AND the murderer who has been killing all those people
Leaper, D’oh! You’re right, of course. (And your spoiler accentuates Ellery’s god complex!)
The whole Wrightsville set of novels was like that, though. In the first one, Calamity Town, Ellery solves the crime in a way that has to be not publicly revealed and this is repeated in The Murderer Is a Fox. That makes the reversal in Ten Day’s Wonder, where the public solution is the wrong one, even more poignant.
He followed that with Double, Double, in which the solution breaks his client’s heart.
Most see the first three Wrightsville books as his best work, along with Cat of Many Tails, because Queen successfully for the time managed to push the formal puzzle mystery past its bounds to reflect a more realistic vision of the effects of murder on family relations. And the whole notion of mysteries creating order in society by using reason to capture and punish the guilty is completely subverted by endings where the public is never given the whole truth, and in fact sometimes given totally false solutions.
In many ways, neither he nor anyone else could take the formal puzzle novel any farther than this, and he and Carr and Christie and that whole bunch faded away with the coming the 1950s. Today, though, when I read mysteries whose solutions depend on a twisted reading of a single line in the book I do miss the old formal puzzles, unrealistic as they might have been.
Calamity Town is my favorite Ellery Queen. I wrote some ginormous dissertation on it at university, but for the life of me I can’t remember what I was nattering on about!
I didn’t care much for anything Rex Stout wrote in the last 10 years or so of his life, but his last Nero Wolfe novel, “A Family Matter,” fits the category.
Wolfe spends much of the novel trying to find a connection between a murder case and Richard Nixon. In reality, the murder had nothing to do with Watergate, and was committed by a longtime employee of Wolfe, a character who’d been appearing in Nero Wolfe mysteries for 40 years.
Damnit, that was gonna be my contribution. 
The movie, I thought, was pretty bad, but it’s worth watching as a contribution to the Faust mythos. It takes it in an original and interesting direction–even if the execution was pretty poor.
Another film example (and not really a mystery eityher), but in The Boondock Saints the detective
actually helps the killers get into a courthouse to kill the mafia don. Although the killers are the protagonists durring the entire movie.