Aaron Reilly and Joshua Brock, both 19, were found unconscious at Pryzm nightclub at around 1.40am on Saturday after taking the substance, Devon and Cornwall Police said.
They were part of a larger group all understood to have taken the drug, but the two teenagers died in hospital shortly after.
Aaron Reilly's family described him as a responsible young man who made "one silly mistake".
"Aaron was a much loved son, brother, grandson and boyfriend. He loved to skate, play computer games. Like most teenage lads he liked a night out with his friends and was respected by them as a non-drug user," they said.
Relatives of Joshua Brock said what happened that night was "so totally out of character as he was always against drug taking in any shape or form".
"One moment of madness led to this tragedy," the family statement added.
An 18-year-old man who was arrested in connection with the incident has been released under investigation, pending further enquiries.
Anyone with information should contact the police on 101 or 101@dc.police.uk quoting log number 67 for December 9, or through Crimestoppers on 0800 555 111.