It marked the first time that a civilian court in Pakistan has sentenced to death a serving member of the military.
Although the Rangers paramilitary technically comes under the supervision of the interior ministry, it is considered part of the powerful armed forces, which has ruled the country for more than half its existence.
The June 8 killing of Sarfaraz Shah, 22, was filmed by a cameraman and broadcast on television, sparking a public backlash over the brutality of trained officers in a country awash with violence blamed on the Taliban and Al-Qaeda.
Judge Bashir Ahmed Khoso read out the verdict before an anti-terrorism court in Karachi, finding Shahid Zafar guilty of pulling the trigger, and sentenced him to death and a fine of 200,000 rupees ($2,300).
"The crime of killing Sarfraz Shah has been proved against you and I announce the death sentence and also impose a fine of 200,000 rupees," said Khoso, addressing Zafar.
He handed life terms to five other paramilitary soldiers and a civilian who had accused Shah of robbery and dragged him over to them. The judge ordered each to pay 100,000 rupees to the victim's family.
The verdict concludes a relatively swift trial which got underway after the seven defendants were formally charged with murder and terrorism on June 29, just weeks after the killing.
So extreme was the public and media reaction to the killing that the government also took the rare step of removing the provincial chiefs of police and Rangers in Karachi.
The widely-aired footage of the killing showed a clean-shaven and unarmed Shah, wearing black trousers and a navy shirt, pleading for his life before he is shot twice.
He then begs for help while the soldiers appear to do nothing but watch him lapse gradually into unconsciousness.
Despite no evidence in the video that Shah was armed, Pakistani Interior Minister Rehman Malik, whose ministry is responsible for the Rangers, had claimed that the victim had been carrying an unlicensed weapon.
The killings last month by security forces of five unarmed Chechens, one of them a pregnant woman, in the city of Quetta are also under investigation.
Answerable to the interior ministry, more than 10,000 paramilitary troops patrol Karachi, Pakistan's financial capital, and its surroundings to combat routine ethnic, political and Islamist violence in the city of 16 million.
Human rights activists condemned Shah's killing and complain that the Rangers, established for combat and border duty, are neither equipped nor trained for civilian areas.