Gaby Scanlon, of Heysham, Lancashire, had to have her stomach removed after drinking the Nitro-Jagermeister shot.
Oscar's Wine Bar in Lancaster admitted at Preston Crown Court to failing to ensure the cocktail was safe to consume after the incident in October 2012.
Charges were also dropped against barman Matthew Harding, from Lancaster.
The firm's director Andrew Dunn, of Old Earswick, York, pleaded not guilty to his part in the company's failings.
The court heard prosecutors would offer no evidence against him if he made a Â£20,000 payment towards court costs before the wine bar's sentencing on 17 September.
The company, registered in Swinton, South Yorkshire admitted one count of failing in the duty of an employer to ensure the safety of persons not in its employment.
A not guilty plea was accepted from bar employee Mr Harding, of George Street, Lancaster.
It had been alleged he presented the Nitro-Jagermeister at the customer's table when it was still producing cold nitrogen gases and was unsafe to drink.
Miss Scanlon, now aged 20, was celebrating her birthday with friends at Oscar's when she drank the shot.
She said her stomach began to expand and a CT scan at Lancaster Royal Infirmary found a large perforation.
The student spent three weeks in hospital as doctors removed her stomach and connected her oesophagus directly to her small bowel.
Welcoming the guilty plea, a statement from her solicitor Patricia Noone said the family hoped the case would serve as a warning to all bars and restaurants to take "take responsibility for what they are serving to members of the public".
It added: "She now suffers episodes of agonising pain and has been hospitalised several times. She has to avoid certain foods and can no longer enjoy eating."
The statement continued that Miss Scanlon cannot work full-time, adding: "She has had to watch all her friends go off to university while she struggles to get her life back on track."
A wine bar where an 18-year-old girl was seriously injured drinking a cocktail containing liquid nitrogen has admitted health and safety failings.