The Premier League giants beat Benfica 4-1 in a match that was delayed for two hours due to lightning and took nearly five hours to complete in Charlotte.
Chelsea advanced to play Palmeiras after they won the all-Brazilian clash against Botafogo 1-0 earlier on Saturday.
Christopher Nkunku's tiebreaking goal came in the 108th minute with Benfica playing a man down after Gianluca Prestianni received a red card. Moises Caicedo's left-footed shot from the left side of the box was saved by Anatolii Trubin, but an alert Nkunku was there to bury the deflection into the top right corner.
Pedro Neto and Kiernan Dewsbury-Hall added insurance goals in extra-time for the final margin.
Reece James scored a free kick in the 64th minute to give Chelsea a 1-0 lead.
But with four minutes left in regulation, the match was stopped. And when the teams returned, Chelsea were called for a handball and Angel Di Maria converted the penalty to level for the Portuguese side.
"Very proud, the performance for me was top until 85 minutes when they stopped the game and it started a completely different game," said Chelsea manager Enzo Maresca.
"When you are inside for more than one hour, it's not easy, but 1-1 and then we continued to play and the reward was the one that we deserved."
In Philadelphia, Palmeiras edged out Botafogo with an extra-time winner from Paulinho in the opening tie of the knockout stage.
At the end of the first half, Palmeiras midfielder Richard Rios forced Botafogo goalkeeper John Victor into a flying save.
Chelsea-bound Palmeiras forward Estevao saw a goal ruled out for offside five minutes into the second half, before Victor tipped over a glancing header from Mauricio.
Palmeiras made the decisive breakthrough in the 10th minute of extra-time when substitute Paulinho cut into the penalty area from the right and clipped a low shot into the far corner.
Botafogo carved out an opening early in the second period of extra-time when Igor Jesus headed over and Vitinho then crashed a volley wide at the far post.
Palmeiras were reduced to 10 men with four minutes remaining when captain Gustavo Gomez was shown a second yellow card following an off-the-ball tussle with Alexander Barboza.
With Reuters.
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