Glasgow were leading the match 3-0 just short of half-time when a security announcement came over the tannoy telling everyone to evacuate the stadium.
Even the broadcast announcers on Sky Sports were forced to leave their positions as spectators emptied from the stands.
A fire alarm caused the evacuation and emergency services were called in.
After a near 30-minute delay the game was allowed to resume with referees and team officials agreeing to forego the remaining two minutes of the first half and restart action with the second period.
Edinburgh won the first game between the sides last week and will clinch the 1872 Cup with a victory.
If Glasgow emerge victorious then it will go to a deciding match between the two, scheduled to take place in April next year.