The Mexican broke the deadlock with a long-range shot and was also involved in the other two goals, scored by Jackson Martinez and Cristian Tello, as Porto, already qualified with two games to spare, chalked up their fourth win in five games.
BATE's fourth defeat in Group H ended their lingering chances of qualifying and meant that second-placed Shakhtar Donetsk (eight points) qualified before that start of their game against Athletic Bilbao.
It would have been an enormous surprise if BATE had gone through after a 6-0 loss in Portugal, and 5-0 and 7-0 defeats against the Ukrainians.
Porto, leaders with 13 points, dominated possession in a first half played in sub-zero temperatures without really troubling Sergei Chernik in the BATE goal.
The visitors were much more efficient after the break and went ahead in the 56th minute when Casemiro won possession about 30 metres from goal and slipped the ball to Herrera who scored with a dipping effort.
Nine minutes later, a typically neat passing move culminated with Yacine Brahimi crossing for Herrera and he laid the ball off for Martinez to side-foot into the corner.
Herrera capped his display by threading the ball through to Tello who cut inside a defender and fired past Chernik, leaving BATE with three points courtesy of their shock 2-1 win over Athletic Bilbao in September.
BATE, full name Borisov Works of Automobile and Tractor Electric Equipment, won the Belarus Premier League for the ninth season in a row earlier this month, and start in the second qualifying round next season.
(Writing by Brian Homewood in Berne; editing by Tom Hayward and Toby Davis)
