The victims had been married for a year and were living in Karachi's eastern Malir district after the woman left her previous husband and fled her home in the city's west.
A tribal 'jirga' or informal council -- which included her first husband and his relatives -- sentenced the pair to death. Holding jirgas is illegal in Pakistan.
"They were strangled and buried in a graveyard by the jirga members," Javed Akbar, a senior police officer told AFP, adding that the men were arrested on Tuesday.
Perpetrators have often walked free because of a legal loophole that allowed them to seek forgiveness for the crime from another family member, but earlier this month the government passed a law that mandates life imprisonment even if the attacker escapes capital punishment via a relative's pardon.