Povetkin, 33, extended his undefeated record to 25 fights with 18 victories coming inside the distance.
The 39-year-old Rahman, who famously relieved Britain’s Lennox Lewis of his world titles in 2001, fell to his eighth career defeat against 41 wins and two draws.
Povetkin defeated Uzbekistan’s Ruslan Chagaeva in 2008 to win the WBA belt and had already defended it with wins over Cedric Boswell and Marco Huck before Saturday’s comfortable win.
Rahman looked a shadow of the fighter who beat Lewis in South Africa in 2001 to claim the WBC and IBF crowns in a stunning fifth round knockout.
Lewis was to regain them in a fourth-round knock-out seven months later.
The Baltimore fighter, nicknamed “The Rock”, then went on to lose to Wladimir Klitschko in 2008 in Mannheim when the IBF, WBO and IBO titles were up for grabs.