Former Manchester City striker Carlos Tevez scored a double in the night's other game as Juventus pulled off an impressive 3-0 win away at 2013 finalists Borussia Dortmund to win 5-1 on aggregate.
For Tevez it represents quite a turnaround in fortunes in the competition, having gone six seasons without a Champions League goal,he has now scored six this term.
"The team played really well, I just do my job and the team deserved the win," said Tevez.
"We showed our experience and I think we're on the right path," added the 31-year-old.
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Rakitic struck with a delightful effort after being found by Lionel Messi, chesting it down and then lofting the ball over the outstanding Joe Hart.
"I think we put in a great effort out there," said Rakitic, after scoring his first goal in the competition.
City had their chances to get back into the game, none more so than when Sergio Aguero was given the opportunity to reduce the overall deficit with a penalty.
However, he failed to take the chance and Barcelona held on comfortably only being denied a more convincing margin of victory by the impressive Hart.
City manager Manuel Pellegrini tried to draw some consolation from the defeat which will cast further doubt over his future at the club as they are struggling to defend their league title with Chelsea six points clear and a game in hand.