Striker Dmitry Kirichenko's opening goal after 67 seconds on Sunday was the fastest-ever in European Championship finals, while the victory was Russia's first in the competition since the demise of the Soviet Union.
But overall it was a case of too little, too late for the Russians, who must now prepare for a World Cup qualifying campaign this autumn. Their group includes Euro 2004 hosts Portugal and fellow finalists Latvia.
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Russia have been dogged by scandal, in-fighting and injuries in recent months.
TITOV BANNED
Things started to go wrong when midfielder Yegor Titov was banned after he failed a drugs test in a Euro 2004 playoff match with Wales last year.
Injuries ruled out defenders Victor Onopko and Sergei Ignashevich on the eve of the tournament. Yartsev then sent home midfielder Alexander Mostovoi, his most senior player, following a row after the first game.
Russia failed to score in defeats to Spain and Portugal and fans criticised Yartsev for being too negative in fielding just one striker.
He switched formations on Sunday and was rewarded with two goals in the first 17 minutes when Kirichenko and strike partner Dmitry Bulykin took advantage of a shaky Greek defence.
Russia are pinning their World Cup hopes on a new generation of young players and can take heartt from assured performances on Sunday by defenders Alexei Bugayev and Alexander Anyukov, both in their early 20s and in their first major tournament.
Russia's victory ended a record nine-game winless streak in the tournament, stretching back 16 years to when the then Soviet Union beat Italy to reach the 1988 European Championship final.
How times have changed. Thousands of fans now follow the team and chants of "Russia, Russia" echoed around the Algarve stadium on Sunday night as they cheered a long awaited victory.