Both teams headed into the contest level on three points in Group B at the halfway stage, with the hosts seeking revenge after losing 2-0 to the Portuguese giants last week.
However, two goals from Taremi and an early opener from Galeno helped Sergio Conceicao's side secure maximum points and climb into second place in Group B, two points clear of Atletico Madrid in third, while Xavi Alonso's men remain at the foot of the group with only three points.
Porto made the perfect start to the contest and opened the scoring in just the sixth minute when goalkeeper Diogo Costa picked out Galeno on the left flank before the winger cut inside and fizzed a low-driven shot into the bottom corner.
Leverkusen's Mitchel Bakker then appealed for a penalty 10 minutes later after being swiped down by Mateus Uribe, but the referee instead decided to book the former for diving. However, following a consultation with the VAR pitchside monitor, the referee reversed his decision and awarded the hosts a spot kick.
Kerem Demirbay stepped up for Leverkusen, but Porto stopper Costa guessed correctly and dived to his left to keep out the midfielder's strike from 12 yards.
VAR was involved again 10 minutes before the interval as Amine Adli thought he had restored parity for the hosts, but his first-time strike from inside the area was disallowed as it deflected off the arm of teammate Patrik Schick.
Both sides came out the blocks quickly in the second half, but Leverkusen's task to get back into the game became much tougher when Taremi doubled Porto's lead from the penalty spot seven minutes after the interval following another VAR review for a foul by Adli on Galeno.
Galeno was brought down again inside the penalty area just after the hour mark after attempting to weave his way past Odilon Kossounou, and the referee pointed to the spot, with Taremi making no mistake again from 12 yards with a coolly-taken penalty into the bottom-left corner.
Leverkusen continued to probe in the final third but they lacked a cutting edge in front of goal, and Porto eventually saw out the game to claim their second successive win in Group B.
Elsewhere in Group B, leaders Club Brugge have secured their place in the Champions League knockout rounds after playing out a goalless draw with 10 men against Atletico earlier this evening.
Porto can join Brugge in the last 16 if they beat the Belgian outfit in their penultimate group fixture in two weeks' time, and if Atletico fail to beat Leverkusen on home soil.