Medhi Taremi scored the only goal of the night with a stunning bicycle kick four minutes into stoppage time, but it was not enough for the away side over the two legs.
Thomas Tuchel's side had come into this match as heavy favourites thanks to their 2-0 victory in the first leg which, despite both ties taking place in Seville due to COVID-19 restrictions, was Porto's home game.
"We accepted what was needed, it was a tough, tough fight," Tuchel told BT Sport.
"Maybe on the television it was not so nice to watch but on the sidelines it was a very intense game, a very fast game. It was very hard to play against them to escape the pressure but with every minute we did it better and better."
With Chelsea in a commanding position and Porto at their strongest when opponents come onto them, there were no shots on target in a fairly uneventful first half.
Porto almost had a chance early on when Chelsea goalkeeper Edouard Mendy controlled a back pass from Antonio Rudiger straight to opposition winger Jesus Corona, who was quickly closed down by Jorginho.
The first effort on target came from the visitors midway through the second half when Corona found Taremi in the box, but the Iran forward's tame header was comfortably saved by Mendy.
Porto impressed with their elimination of Juventus in the round of 16, but Taremi's goal came too late in the tie for it to have any real significance.
Porto coach Sergio Conceicao praised his side for going toe-to-toe with Chelsea.
"I am extremely proud of the group, the players and the way they believe in what they work for. It was one of the best games I have been involved in in Europe. It had everything.
"We were very competent in defensive organisation against a great opponent... we did not let Chelsea's players, who are of the highest level, create many chances."
Goalscorer Taremi added: "We played a great game, we showed that we are a great team, but unfortunately my goal wasn't enough."
Chelsea have reached the last four for the first time since 2014, having won the Champions League two years earlier.
"We're buzzing, it doesn't get better than that," said Chelsea's Mason Mount.
"We could have played better but just getting through was at the forefront of our minds and we did that tonight. "We knew as a team we had to work our socks off. We knew what the final result was if we won."