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Chelsea claimed a 2-0 victory over the Portuguese side in the first leg of their quarter-final clash at the Ramon Sanchez Pizjuan last week.
Porto might have been knocked out due to the aggregate scoreline, but Taremi ensured that his side walked away as the winners of the second-leg tie.
Nanu managed to pick out Taremi with a cross from the right and the Porto striker smashed an incredible bicycle kick past a helpless Edouard Mendy.
Chelsea will now progress to the semi-finals and will face the winner of Real Madrid vs Liverpool.
Chelsea boss Thomas Tuchel insisted that reaching the semi-finals was a "big achievement," especially after Chelsea's recent run of fixtures.
The 47-year-old German told BT Sport: "You can always feel when the pressure is on but we are used to it.
"We have played Manchester United, Liverpool, Everton and Atletico Madrid in two weeks. All of these matches are every three days.
"We did not talk about the result in the first game. We talked about what we needed to do if you feel nervous and that is to use your body, work hard and make yourself sweat.
"This is what we did. We tried to give them confidence and show them what they should do as a team.
"It is nice for them I think as they know they can rely on each other, which is the most important thing. We will become a strong side. The semi-finals is a big achievement."
Meanwhile, Champions League holders Bayern Munich were knocked out of the quarter-finals by Paris Saint-Germain.
Eric Maxim Choupo-Moting sealed a 1-0 win at the Parc des Princes on Tuesday, but PSG progressed to the semi-finals on a 3-3 aggregate scoreline.
The two-leg Champions League semi-final matches will be played in April and May.
Liverpool, who suffered a 3-0 defeat to Madrid in the first leg, will welcome Los Blancos to Anfield on Wednesday for their second-leg quarter-final clash.
Manchester City, meanwhile, will play Borussia Dortmund at the Westfalenstadion tomorrow in their second-leg tie.
Featured Image Credit: BT Sport/Twitter
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