Ukraine, winners at Athens 2004 and Beijing 2008, had started the tournament as favourites and lived up to that billing as they came through the group stage in style.
However, in the showpiece Ramonov's strike was all that separated the sides, as Russia exacted revenge for their final defeat four years ago.
It was no less than the Russians deserved as they dominated throughout.
They had a string of early chances, with Zaurbek Pagaev heading narrowly wide before stumbling at the crucial moment when he was played in by captain Ivan Potekhin.
A curling effort from Viacheslav Larionov was palmed away before Pagaev blasted a shot into the side-netting.
The only serious Ukraine attack of the first half ended with Volodymyr Antoniuk's shot being deflected wide for a corner.
Russia continued to dominate in the second half, with Ramonov going close to playing in Pagaev and forcing goalkeeper Kostyantyn Symashko to come and smother on the edge of his area.
Anatolii Shevchyk went close with a rare chance for Ukraine, shooting narrowly wide from the edge of the area before Volodymur Antoniuk almost got lucky with a low drive that struck Lasha Murvanadze and went narrowly wide.
But Russia got the breakthrough they deserved with 16 minutes left when Pagaev's flick-on allowed Ramonov to race through and slot it beyond the goalkeeper.
Earlier, three goals in the space of seven first-half minutes powered Iran to bronze with a 5-0 win over Brazil.
Rasoul Atashafrouz scored either side of a fine strike from Farzad Mehri, and Iran then took advantage of an increasingly stretched Brazil side to add late goals from Jasem Bakhshi and Mehri again.
In a rematch of the 2008 bronze-medal game, Iran's winning margin was one better than their 4-0 win in Beijing.