The emotional effects of victory and even qualification for a major tournament may help strengthen national identity in countries where it is lacking, they argued.
The study, published last month by the National Bureau of Economic Research, suggested a feel-good factor from big-match wins can improve trust between ethnic groups and cut unrest.
"The effect is sizeable and robust and is not explained by generic euphoria or optimism. Crucially, national victories do not only affect attitudes but also reduce violence," it added.
Ruben Durante, a political economist at the Paris Institute of Political Studies who co-authored the paper, said there were many examples about how sport had brought nations together.
In 1980, US resolve in the Cold War was hardened by an improbable ice hockey victory against the Soviet Union at that year's Winter Olympics.
In 1998, France's World Cup football-winning side were held up as a model of racial integration at a time of tensions about immigration.
South African president Nelson Mandela's use of the 1995 rugby union World Cup was designed to help heal a fractured nation emerging from decades of apartheid.
On the other hand, sport can lead to bloodshed: an ill-tempered qualifying match between El Salvador and Honduras for the 1970 World Cup sparked rioting that led to a brief border conflict known as the "Football War" of 1969.
The study -- "Building Nations Through Shared Experiences: Evidence From African Football" -- analysed more than 70 Africa Cup of Nations and World Cup qualifying matches in sub-Saharan Africa between 2000 and 2015.
It matched them with answers to Afrobarometer surveys about national and ethnic identity conducted before and after games from more than 28,000 respondents in 18 countries.
The authors then compared data on violence in those countries.
"What we found is that experience of a win in one of those high-stakes matches (indicated) people are less likely to report ethnic over national allegiances," Durante told AFP.
Different ethnic groups became more trusting of one another and the positive effects lasted over time, he added in an interview.
The effect was seen particularly in victories against a traditional rival and when the national team was more ethnically diverse.
The greater sense of belonging that produced was most pronounced in areas where there was little visible state presence in terms of infrastructure.
Defeats, in contrast, did not give the opposite effect and there was no difference as to whether the victory was at home or away, the study suggested.
But it warned politicians hoping to jump on the bandwagon of success to be wary, as there was no corresponding increase in support for the ruling party or incumbent.
'Window of opportunity'
On the reduction of violence after national team victories, the paper said the effect was most seen in nations whose teams scraped through qualifying, were not expected to go through or who had not reached a finals for a long time.
"Nations whose teams barely qualified actually experienced a decline in conflict over the following six months," said Durante.
Durante said countries needed to be wary of the dangers of using greater national identity negatively, citing Hitler's use of the 1938 Olympics as a vehicle to champion Nazism.
But the findings indicated that in countries hit by tensions about identity, sport -- or any shared experience where people have a deep emotional investment -- can be beneficial.
"You can open a window of opportunity that people feel part of a nation and bring people to the table," he added.