The micro state's national team, which achieved their first competitive victory against Liechtenstein in September, has earned promotion by finishing at the top of Group D1.
"Finishing that first half 1-0 down was an insult to football, but the boys were brilliant and deserved what they've managed to achieve," said San Marino coach Roberto Cevoli.
San Marino are international football's bottom-ranked team but finished the group one point ahead of Gibraltar with whom they drew 1-1 on Friday thanks to a last-gasp Nanni spot-kick.
They scored three goals in an official fixture for the first time and Golinucci's first-time finish in the 76th minute, which decided the match, came from a slick passing move which would have once been unthinkable.
"Apart from suffering the serious risk of heart attack, all I can say is that these boys made history tonight," said a visibly emotional Marco Tura, the president of the San Marino Football Federation.
"As people, as athletes, as men they have shown what they are worth... I cried with the boys."
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The whipping boys of international football had been building up to their historic Nations League campaign after also claiming draws in friendly matches against Seychelles, Saint Lucia and Saint Kitts and Nevis over the last two years.
(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)