Hundreds of fans from both teams ran on to the pitch at the end of the match.
The ugly scenes, broadcast live on television, will not do Yekaterinburg any favours as the Ural city is bidding to host matches at the 2018 World Cup in Russia.
According to local media reports, there was also a scuffle between Dynamo's Australian midfielder Luke Wilkshire and two Rubin players, Finland midfielder Eremenko and Spanish defender Sezar Navas, in the tunnel after the game.
Rubin won the trophy for the first time after Eremenko beat keeper Anton Shunin with a low shot from 30 metres.
"We really wanted to win this to complete our set of (domestic) trophies," coach Kurban Berdyev told Russian television.
Berdyev also guided Rubin to back-to-back league titles in 2008 and 2009.
The result means Rubin, beaten Cup finalists in 2009, will play in the Europa League next season.
Dynamo, who finished fourth in Russia's Championship Group play-off, will also play in Europe's second-tier competition on account of their league position.
Rubin's victory means Lokomotiv Moscow miss on a European place: they would have qualified for the Europa League had city rivals Dynamo won.