Final answer:
The Supreme Court case that established the 5th Amendment's self-incrimination protection in state courts is Miranda v. Arizona, requiring suspects to be informed of their rights before interrogation.
Step-by-step explanation:
The Supreme Court case that held that the 5th Amendment's self-incrimination clause prevents the admission of involuntary confessions into evidence in state courts is Miranda v. Arizona, 384 U.S. 436 (1966). The historical ruling determined that prosecutors could not use statements from custodial interrogation of defendants unless procedural safeguards effective to secure the privilege against self-incrimination were demonstrated. Key to this case's decision was the requirement that suspects must be informed of their rights - notably, the right to remain silent and the right to counsel - prior to interrogation, ensuring that any confession obtained is voluntarily given and that the suspects understanding of their Fifth Amendment rights.