A man was charged with assaulting police, while another man was charged with assault.
Acting Superintendent Mick Rochester, commander of the group of officers policing the event, said those arrested would face hefty fines and could be banned from attending events at the stadium.
He said it was disappointing that the drunken anti-social behaviour of a few marred the night for many of the 17,000-plus spectators.
Twenty-seven people were ejected for being intoxicated, while 47 people were refused entry because of drunkenness.
Five people were issued infringement notices for failing to leave when asked, with one of those subsequently arrested.
The Mariners beat Celtic, Scottish Premier League runners-up, 1-0.
'The message is a simple one - anti-social and criminal behaviour will not be tolerated under any circumstances," acting Superintendent Rochester said. ''If you can't or won't heed the message, don't attend these events. A sporting event is not an excuse to break the law.
'If your team isn't performing well, or you disagree with a decision by the referee, you can't react by getting intoxicated, damaging property, assaulting others or making an idiot of yourself.
'Be warned. Police and event security staff will continue to act swiftly at sporting and other events to ensure any opportunities to disrupt the enjoyment of others are minimised.'
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