The Portuguese side took the lead in the fifth minute when the visitors' keeper Sergey Chernik threw the ball out of the box straight into the path of Brahimi, and he made no mistake firing it into the top corner.
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BATE almost responded immediately when Mikhail Gordeichuk showed a great burst of pace to break from midfield and he got into the box. However, Fabiano raced out of his goal to narrow the angle and make the stop with his feet.
Jackson Martinez should have doubled the home side's lead when he latched on to a ball from Brahimi at the back post, but his chipped effort smacked off the post and bounced clear.
Brahimi did double his side's lead with an individual goal as he raced the length of the pitch and weaved his way inside the box before powering an effort past Chernik into the net.
Porto continued their dominance as they netted for a third time when Danilo beat a poor challenge down the right and whipped a dangerous cross to the near post, which was converted by Martinez.