Luiz levelled with four minutes left with a powerful header after Gary Cahill's 81st-minute opener and Silva made it 2-2 with a looping header after Eden Hazard had given the hosts the advantage from the spot.
The result was enough to send 10-man PSG through to the quarter-finals on away goals.
It was redemption for Silva as it was his handball that gave Premier League leaders Chelsea the penalty in extra-time which Hazard coolly converted.
Silva was, however, full of praise for the whole team.
"This goal is not a personal revenge," he said. "I was very happy to score but especially for the team because it rewarded us for a great game after playing with one less man."
"Thiago Silva and David Luiz are world class players, I'm happy to have them with me," said Zlatan Ibrahimovic, who was sent off in the 31st minute.
Former Chelsea defender Luiz's price tag of 50 million pounds has often been mocked at as he suffered lapses of concentration that cost PSG more than once, while Silva's first part of the season suggested the 'Monster' had not fully recovered from the World Cup trauma, when hosts Brazil were eliminated in the semi-finals with a 7-1 defeat to Germany.
Yet, on Wednesday, both were remarkable for PSG, who were probably counting more on Ibrahimovic to score after a 1-1 draw in the first leg had left the French club in an uncomfortable position.
But the Sweden striker, who has often been a pale shadow of his brilliant self, was once again disappointing, showing very little until he was sent off for a tackle on Oscar.
His absence barely unsettled PSG, who also had a steely midfield of Thiago Motta, Marco Verratti and Blaise Matuidi to thank for as they stayed afloat.
"It was amazing tonight, the spirit, the players gave everything. When we lost Ibra we said we had to keep it simple and keep the ball," said Luiz.
According to Verratti, Ibrahimovic's sending-off gave PSG extra motivation.
"We had a big desire to win this game, but after Ibra's sending-off, we were even more motivated," the Italian said.
(Editing by Sudipto Ganguly)
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