Rakitic, who came on following an injury to Sergi Roberto after just 17 minutes, hit a sublime strike into the top corner having been set up by Neymar at the start of the second half.
A livewire Neymar led Barca in the absence of the injured Lionel Messi but while they had plenty of possession they lacked a cutting edge in the first half.
Neymar was again the provider after 64 minutes for Rakitic who sealed the win with a clinical finish past keeper Sergey Chernik.
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Barca laid siege to the BATE defence in the opening minutes, starting with a strike from Neymar from the left of the area saved by Chernik.
Luis Suarez had a header tipped over and then Munir El Haddadi, preferred to Sandro Ramirez in attack, should have scored but his shot was too weak and the keeper blocked it.
Barca continued to push forward but too often their final pass was poor while BATE offered little danger at the other end.
Rakitic, who was surprisingly left out with Javier Mascherano starting in midfield, missed a glaring chance when, unmarked, he headed over the crossbar before the break.
He made up for it with his excellent strike on 48 minutes and then clipped the ball over Chernik from close range for his second on the night.
“I was glad to help team and the most important thing was that we got the victory. It is not easy to play here in these conditions and the cold,” Rakitic told reporters.
“I think it was (our most complete game this season) as we were solid at the back and gave away few chances, while in attack we worked hard and maybe just lacked another goal. We are on the right lines.”
Barca have seven points from three games and BATE have three.
(Reporting by Tim Hanlon in Barcelona, editing by Clare Lovell)
