Seydou Doumbia beat Anzhi keeper Vladimir Gabulov with the spot kick that secured victory in the shootout and a first league and cup double in seven years for CSKA who lifted their seventh Russian Cup and 12th including Soviet-era triumphs.
Leonid Slutsky's CSKA side, who were crowned Russian champions last month, took an eighth-minute lead through Ahmed Musa before Anzhi pulled level through Lassana Diarra's stunning 74th-minute strike from about 25 metres.
The French midfielder was given time to switch the ball on to his left foot before unleashing a devastating shot that cut through the CSKA defence and whizzed over the head of goalkeeper Igor Akinfeyev, who barely moved, into the top of the net.
With both keepers making a series of good saves in extra time, neither side could find a breakthrough and penalties followed in Grozny, capital of Russia's Chechnya region and the site of two devastating post-Soviet separatist wars.
Anzhi, managed by Guus Hiddink and chasing a first major trophy, missed two spot kicks with Akinfeyev deflecting Yuri Zhirkov's effort and Jucilei da Silva shooting wide, while Nigerian Musa was the only CSKA player to fail.