The trio of Timur Safin, Alexey Cheremisinov and Artur Akhmatkhuzin trailed for long spells but fought back to secure Russia's third gold of the fencing events - and sixth in total.
The United States took the bronze medal with a 45-31 victory over defending champions Italy.
The US now have three fencing medals at these Games, level with Hungary.
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Russia beat France 45-41 to win the men's Olympic foil team gold medal on Friday.