A federal appeals panel on Tuesday overturned the 2015 corruption convictions of Dean G. Skelos, once the powerful majority leader of the New York State Senate, and his son, Adam B. Skelos, toppling the final bookend of what had been historic, back-to-back convictions of two of Albany’s most entrenched leaders.

In ruling in favor of the Skeloses, the judges — just as another appellate panel did in July for Sheldon Silver, the former longtime Democratic speaker of the State Assembly — cited a decision last year of the United States Supreme Court that narrowed the legal definition of corruption in a case that involved Bob McDonnell, the former Republican governor of Virginia.

The convictions of Mr. Skelos and Mr. Silver had heralded a deathblow to the culture of corruption in Albany, sending a signal that no politician in New York was immune from the scrutiny of Preet Bharara, then the United States attorney in Manhattan.

But in the McDonnell opinion, the Supreme Court made it harder for prosecutors to prove corruption. The court ruled that only formal and concrete government actions or decisions could serve as a basis of a corruption prosecution, and not political courtesies like setting up a meeting.