Extra time was looming at Lincoln Financial Field on Friday until Malo Gusto's cross took deflections off Agustin Giay and goalkeeper Weverton and ended up in the back of the Brazilians' net in the 83rd minute.
The London side had led early on through Cole Palmer but were pegged back by a superb strike from Estevao Willian, the 18-year-old winger who will join them after the tournament.
Palmeiras had been threatening to finish the stronger but Gusto's late stroke of luck ensured it was Chelsea who went through to face Fluminense, 2-1 winners over Al-Hilal earlier, in the last four.
The contest was played in vibrant atmosphere with the crowd, perhaps helped by the dynamically-priced tickets having dropped as low as £8 earlier in the day, an impressive 65,782.
Pedro Neto started despite having considered missing the game following the death of his Portugal teammate and Liverpool striker Diogo Jota, and he held up a shirt bearing his name and that of his brother Andre Silva during a pre-match moment's silence.
Palmer had already forced a good save from Weverton when he opened the scoring following a fine run and finish on 16 minutes.
The England international wrong-footed a defender with a quick turn and he then swerved past another challenge before delivering a left-foot shot into the bottom corner.
Chelsea could have increased their lead as Marc Cucurella and Enzo Fernandez tested Weverton and Trevoh Chalobah and Christopher Nkunku missed the target.
With Cucurella giving Estevao a tough time until this point, Palmeiras struggled to create openings.
They finally threatened just before the interval but Robert Sanchez comfortably saved Vanderlan's header and Bruno Fuchs nodded over after the restart.
It proved the start of a good spell for the Sao Paulo side and the equaliser came as Estevao took a pass from the right and lashed in a shot from a tight angle.
It was a stunning finish and Chelsea immediately responded by sending on Joao Pedro for his debut following his move from Brighton.
Chelsea had a scare when Allan drove narrowly wide and Levi Colwill needed to make a last-gasp interception prevent another Palmeiras chance.
But they had a good opportunity themselves when Cucurella shot over and then edged in front when Gusto's cross took a ricochet and fooled Weverton.
Chelsea now face Fluminense in the semi-finals in New York on Tuesday.
The tournament underdogs struck first through Matheus Martinelli in the opening half before Al-Hilal hit back after the break when Marcus Leonardo found the net.
But Fluminense refused to be denied and regained their lead in the 70th minute through Hercules to secure a memorable win over Al-Hilal in the first meeting between the clubs.
Al-Hilal had announced themselves in the footballing world when they beat Manchester City 4-3.
The late Jota and his brother Andre Silva were honoured with a pre-game moment of silence.
Cameras showed Al Hilal starters and Portuguese compatriots Ruben Neves and Joao Cancelo fighting off tears during the observance.
with PA
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