After a goalless first half, Serb Nikola Drincic shot Amkar ahead from the edge of the box before Tomislav Dujmovic touched in from a corner to double the lead in the 64th minute.
But CSKA hit back immediately thanks to a Vagner Love goal, before fellow Brazilian Jo squared proceedings in the 74th minute and took the game into extra time.
Ironically it was Drincic and Dujmovic, the two players who gave Amkar their two goal lead, who missed the decisive penalties in the shoot-out, the former striking wide and the latter's spot kick saved by Igor Akinfeev.
Pole David Janczyk then struck the winning penalty to give CSKA a 4-1 win.
The army club lift the trophy for the fourth time, whilst Amkar, appearing in their first major final, leave empty handed without even the consolation of a UEFA Cup berth, which will now go to the fourth-placed side from last season's Russian Premier Liga, FC Moscow.