The result leaves the two-time European champions at the top of the Group H table.
Here, Sports Mole takes a closer look at the match.
On target: 12
On target: 2
Was the result fair?
The result was absolutely fair as Porto really were the only side in the match. Although the visitors made a bright start, their heads dropped as soon as Brahimi scored the opener just five minutes in, and they never looked like getting back into contention. Despite being three goals up at half time, Porto never sat back and could easily have won by a greater margin, so certainly were not flattered by the scoreline, which is their record win in their Champions League.
It is difficult to gauge whether Porto were superb or BATE were just that bad, but the hosts looked unbeatable. From the opening moments of the tie, Martinez and Brahimi looked dangerous up front, and they never took their foot off the gas even in stoppage time despite having the match in the bag. There were a couple of moments when Fabiano did not look entirely comfortable between the posts, but he was not called upon too often.
One word sums up BATE's performance this evening: woeful. The Belarusian champions were completely played off the pitch, could barely string three passes together for most of the match, struggled to clear their own penalty area and gave away the ball countless times; it really was a dreadful display. Borisov always looked like being the whipping boys of the group on paper, and they did little to dispel that tonight.
Sports Mole's man of the match
Yacine Brahimi: The Algerian international was just unstoppable tonight. He capitalised on a couple of sloppy defensive errors in the first half, producing brilliant finishes on both occasions, before completing a stunning hat-trick after the break with a flawlessly-taken free kick. Brahimi was not just looking for goals this evening though, as he tried to create a number of chances for Jackson and won the ball back in midfield a number of times for the hosts.
Sergey Chernik was actually one of the best players for BATE this evening, making a series of saves to prevent the visitors from suffering an even heavier defeat, but one of his first touches of the ball was just awful. The goalkeeper threw the ball when Martinez fired wide inside the opening couple of minutes, but got the throw all wrong, landing it at the feet of Brahimi for the winger to fire in his opening goal. After that, the team's heads dropped and the goals kept coming for Porto.
It was a pretty anonymous evening for Bas Nijhuis, as the Dutchman had relatively few decisions to make. He booked just two players - both for BATE, and neither could have had too much cause for complaint - and faced one penalty appeal, but the replays confirmed the official's suspicions that Danilo made the most of it.
Porto: Porto host Boasvista in the Primeira Liga at the weekend, and will travel to Shakhtar Donetsk in their next Champions League outing at the end of the month.
BATE: BATE face their main Belarusian Premier League rivals Dinamo Minsk on Monday as they look to maintain their 22-match unbeaten run in the league, and will host Athletic Bilbao later in the month.