Rakitic's brace after coming off the bench has seen the Spanish side take control of Group E on seven points.
Barcelona have also now won each of their three meetings with BATE and failed to concede in the process.
Here, Sports Mole has dissected the 90 minutes of action between the two teams.
On target: 1
On target: 6
Was the result fair?
In truth, Barcelona will not have many more comfortable games all season. One look at the scoreline would suggest that it was a fairly tight game in Belarus, but that was just not the case. Statistics rarely paint a false picture in football and the fact that the away side had 21 attempts to BATE's four is an indication of what occurred at the Borisov Arena. The hosts did not test Marc-Andre ter Stegen until the second period and the German goalkeeper could have had the night off such was his inactivity.
It threatened to be a difficult second period for the European champions after failing to score in the first, but Rakitic's effort just three minutes after the restart placed a different complexion on the match. When the Croatian made it 2-0, it was game over, but in fairness to BATE, they did have a go in the final five minutes when Barcelona's own tempo dropped. It is often said that no away games in the Champions League are easy, but this was very, very comfortable for the Catalan outfit.
Having beaten Roma 3-2 in their last Champions League match, much was expected from BATE in this one. They were far from favourites entering the fixture, but the manner of the defeat will have disappointed the home supporters. From the first whistle, the Belarusian outfit took up a defensive shape and that was a position they held throughout the contest. With the score still level at the interval, it was a tactic that looked to be working, but Rakitic's first goal certainly changed things.
BATE simply did not create a chance of note in the first period and when they stood off Rakitic in the 48th minute, the Croatian rattled one into the top of the net. The game's second goal was always going to be important, but that also came for Barcelona following more excellent work from man of the match Neymar. Finally BATE had a shot on target 12 minutes from time, but Nikolai Signevich, who had the difficult task of leading the line, could not test Ter Stegen with an effort from outside the box.
It took the home team until the 80th minute for them to start playing, but by that point, it was far too late. Losing to Barcelona is no disgrace, but they went down without a fight in Belarus, which will only leave them with regrets. On the whole, they defended pretty well and worked hard to close the space, but it was never a match that they looked capable of winning. It does not get any easier for BATE, however, as their next group fixture is the reverse at Camp Nou.
It is true that Barcelona are just not the same team without Lionel Messi, but Luis Enrique still has a number of excellent players at his disposal. Alterations were made - four in total - from the weekend and there was a start in attack for Munir El Haddadi, who replaced Sandro Ramirez. Javier Mascherano also moved into a midfield role, but it was not really a match where Barcelona needed two defensive midfielders or three if Sergi Roberto, who went off injured, counts in that position.
It took just four minutes for the Catalan side to create the first clear chance, but Neymar, who was a menace all evening, could not beat Sergei Chernik from a tight angle. Munir and Sergio Busquets also came close to opening the scoring in what was a strong start from the visitors, before Rakitic headed over the crossbar in the latter stages of the first period. It was Neymar that twice set up Rakitic in Belarus, with the midfielder finding the top corner early in the second half, before producing a super finish in the 64th minute for 2-0. At that point, Barcelona were so comfortable and drifting to all three points.
Both managers made changes as the match drew to a close, but it was the visitors that continued to look the most likely to add to the scoring. Neymar and Suarez both had opportunities for three and four, but it was another night of wasteful finishing from the Catalan outfit, despite securing all the points. As comfortable as Barcelona were, BATE were really disappointing and the Spanish giants will need to improve on this performance as they advance deeper into the competition.
Sports Mole's man of the match
Neymar: Rakitic will certainly get the headlines after hitting a brace, but it was Neymar that stole the show. The Brazilian caused havoc from the first whistle as he cut in from the left and on another night, he would have had a couple of goals. Two assists arrived for the 23-year-old, however, as he twice set up Rakitic in the second period. BATE just could not live with the performance of the former Santos attacker.
It is difficult to be too critical of BATE's defensive performance on the night, but the way that their back four stood off Rakitic early in the second period was really poor. When Neymar cut inside his full-back, he had plenty of time to pick a pass into Rakitic, who was not closed down as he sent the ball into the back of the net. It was just too easy for the midfielder to open the scoring in Belarus.
Referee Jorge de Sousa was certainly not afraid to produce cards in Belarus as he issued nine in total, six of which were for the hosts. The Portuguese was guilty of being overly picky in the first half when it came to challenges and indeed bookings, but he was prepared to let the game flow in the second period. Meanwhile, there were not really any major incidents that needed addressing.
BATE: The Belarusian champions return to league action at home to Naftan on Sunday.
Barcelona: Barca's next La Liga clash is at home to Eibar on Sunday.