Their victims were kidnapped from a bar called Heaven not far from the city's main avenue, Paseo de la Reforma.
Their bodies were found three months later in a mass grave outside the city, after family members organised large street protests.
Prosecutors say they are still questioning dozens of other suspects.
The three men who were sentenced were also fined more than $300,000 (Â£197,500) each.
According to the investigation, the crime was a reprisal for the murder of a drug trafficker which occurred a few days before in another bar in Mexico City.
Seven young men and five women ranging between 16 and 34 years of age were reported missing in the days after the group went to the bar in May 2013.
Surveillance footage showed some of them being led to cars outside the after-hours bar.
There was no obvious sign of force on the surveillance footage. The men who took them away were not masked and did not seem to be carrying weapons.
There was no trace of the missing people until their bodies were discovered in a grave covered with lime, cement and asbestos on the outskirts of Mexico City.
All of them came from the rough Tepito neighbourhood of Mexico City.
The case had horrified the people of Mexico City, which at the time had appeared to be less exposed to the overt drug violence affecting other areas of the country.
A Mexico City judge has sentenced three men to 520 years in jail each for their roles in the kidnapping and murder of 13 young people two years ago.