After a slow-paced first half, Hector Herrera lit up the contest with a swerving long-ranger before Jackson Martinez and Cristian Tello added gloss to Porto's performance and consigned BATE to the history books for the wrong reasons.
The Belarusians have now conceded 22 goals in this season's group stage, equalling the previous record set by Dinamo Zagreb and Nordsjaelland, with a game to play against Athletic Bilbao.
Porto came into the game already qualified from Group H, but victory - coupled with Athletic's win at Shakhtar Donetsk - confirms their place as pool winners, potentially easing their task in the last 16.
Lopetegui said: "We won three points in a complicated game against a good team, who came into this game very motivated.
"It's not easy to beat BATE in Borisov, even more so because they wanted to put on a show for their fans.
"We approached this game the right way, it was very important to us.
"The players knew this and worked to win three important points.
"We have created spaces, had initiative and showed personality above all.
"I think in the second half, in which we were very good, we showed an excellent response.
"We have much work to do, of course, but the more time passes, the better for the team.
"Our level of intensity, commitment and attitude, we have been very well throughout the season.
"BATE had conceded many goals so far and people thought it would be easy, but the important thing is that we got three points and we must now move forward."
