And a medallion presented to the winners could be the oldest existing trophy in world football.
Now the medallion, on loan from The Argyll and Sutherland Highlanders Museum in Stirling, will go on show at a football exhibition that opens in Glasgow's Kelvingrove Art Gallery and Museum on March 27. Tickets go on sale tomorrow.
The five-month exhibition, More Than a Game: How Scotland Shaped World Football, will remind visitors of the historical firsts the Scottish game can lay claim to.
Richard McBrearty, curator of the Hampden-based Scottish Football Museum, told the Sunday Herald: "We've known about the game for quite some time. It was played between the regimental team of the 93rd Sutherland Highlanders and the Edinburgh University Football Club, and it was agreed that the losers would present a medal to the winning side.
"Six months ago we wondered what were the chances of the medallion having survived and, if it did, where we could find it. It was a matter of checking that the 93rd Highlanders became the Argyll and Sutherland Highlanders.
"Military museums have fantastic collections and we emailed the Argylls, and they replied with a picture of the medallion.
"From my perspective, as the losers gave the winners a medallion, I would define this as a competitive game and the medallion as a trophy. People today think of trophies as twin-handled pots, but some trophies take the form of shields, or glass vases. In cricket, the Ashes is a tiny urn. We look at this in the wider definition of something being presented to the winning team after a competitive game.
"From my knowledge of football history, I have never come across anything earlier than 1851 in terms of a trophy. It even predates association football. In the UK, there are things like the first Sheffield Rules trophy, the Youdan Cup, but that dates from 1867."
McBrearty said the exhibition would also include the oldest football in the world, which is some 450 years old, and original documents relating to the founding in 1824 of the world's first known football club.
Glasgow was also the birthplace of international football, with a goalless draw between Scotland and England at Partick in 1872.
l Tickets for the exhibition are available from tomorrow from the Kelvingrove shop, online at glasgowmuseums.com or by phone on 0141 353 8000. Prices: Adult £5; concession £3; under-16s go free.
Five-a-side and 11-a-side teams can buy four tickets and get one free, or buy nine and get two free; adult and concession tickets can be combined in any one transaction. Under-16s and five-a-side tickets can only be obtained in person from Kelvingrove.