CCTV footage captured the moment the male victim had the imitation firearm pressed against his head as cries of “shoot him” were made.
During the disturbing incident, which took place in the centre of Briggate, the female victim was told: “Come with us or we will shoot you.”
A court heard police arrived on the scene and arrested the robbers before the incident could get any more “sinister”.
Jack Ward, 20, was jailed for seven years. His 16-year-old accomplice, who cannot be named, was locked up for four years.
The judge who sentenced the pair at Leeds Crown Court described the attack as “a case of the greatest seriousness”.
Stephanie Hancock, prosecuting, said the victims were students at Leeds University and had been to a formal black tie event earlier in the evening.
They were on their way home when they were targeted at around 3am on March 3 this year.
The camera footage showed Ward and the teenager, both wearing hoodies, approaching the couple as they were walking down Briggate.
The couple were initially laughing and joking with the pair.
Miss Hancock described how the incident turned sinister when Ward asked the male victim if he wanted to buy a gun.
Ward then pulled what appeared to be a pistol out of his pocket. The couple were then threatened and the female victim had her clutch bag grabbed from her.
The male victim tried to diffuse the situation but had the weapon pointed to his forehead.
The court heard he believed the weapon to be real and feared he was going to die.
Miss Hancock said he then took the decision to run off in the hope of finding a police officer.
Ward and the teenager then turned their attention to the young woman. The footage showed her being “manhandled” as she cowered in terror in a shop doorway in her evening dress.
Ward then said to her: “Come with us or we will shoot you.”
Police arrived on the scene and arrested the pair as Ward tried to hide the fake gun in a telephone kiosk. The youngster was also found in possession of a knife.
Describing the attack, judge Rodney Jameson, QC, said: “That must have put the worst possible fears in to her mind.”
“It must have been terrifying. There was undoubtedly degradation of both victims. It was at night in the city centre where people are entitled to feel safe.”
Earlier in the evening the pair had attacked another man from behind before stealing his wallet after he was knocked to the ground.
Ward, of Newhall Croft, Belle Isle, and the youth both pleaded guilty to robbery, attempted robbery and possession of an imitation firearm with intent to cause fear of violence.
The youth also admitted possession of a bladed article and further offences of robbery and common assault in relation to a gang attack on a man in the Beeston area of Leeds in August last year.
The youngster has several previous convictions for violence and robbery. At the time of the attack he was subject to a community order after threatening to punch an 11-year-old girl before taking her mobile phone.
Kenton Sargeant, for Ward, said his client had been drinking before the incident and could not remember committing the offence.
Mr Sargeant said Ward was ashamed and sorry for what he had done.
Judge Jameson told the pair: “I’m afraid the time has come for a substantial custodial sentence.”