Armento, 51, of Yonkers, was convicted of first-degree murder while committing a felony. He faces life in prison without parole at his Nov. 14 sentencing.
The jurors in state Supreme Court in the Bronx reached their verdict on the second day of deliberations, after a two-week trial.
Authorities said Armento and Brancato broke into a basement apartment to steal prescription drugs after a night of drinking at a Yonkers strip club. Enchautegui, who lived next-door, came out to investigate at 5 a.m.
Seeing the men, the off-duty officer shouted: "Don't move!
Don't move!"
Prosecutors said Armento fired at the 28-year-old officer with a blast from his .357 Magnum, hitting him once in the heart. The dying officer fired back, striking and wounding both men.
A nurse's aide who testified said that in his hospital bed, Armento bragged about killing a police officer, saying the action would make him "a king in jail."
On Thursday, the jurors acquitted Armento on a separate charge of intentional murder of a police officer - a conviction some NYPD officers had hoped for.
The 32-year-old Brancato, who appeared in the 1993 movie "A Bronx Tale" with Robert De Niro as well as in "The Sopranos," is to be tried on second-degree murder charges next month.