Having suffered a 3-1 defeat in the French capital last week it looked a big ask for the west Londoners to progress from their quarter-final against the big-spending Parisians.
However, substitute Andre Schurrle gave Chelsea hope in the first half and fellow replacement Demba Ba - a boyhood PSG fan - netted late on to secure a 2-0 win that saw them progress on away goals, with the tie ending 3-3 on aggregate.
It stretches Mourinho's unbeaten run in European quarter-finals to nine and, having won the tournament with Porto and Inter Milan, raises possibility of Chelsea repeating their 2012 success.
"We are in the semi-finals and if the quarter-finals had eight fantastic teams, imagine the four that are going to reach the semi-finals," Mourinho said. "Anything can happen.
"A big opponent is waiting for us in the semi-final, but I think it doesn't matter who.
"They know that we are a team with a special spirit, even if we are not in the maximum of our potential.
"[Nemanja] Matic and [Mohamed] Salah cannot play in the Champions League and we always have somebody suspended. It was Ramires today, the next one is [Branislav] Ivanovic.
"But, for sure, we are going to enjoy the same way I told the players we had to enjoy this second leg in the quarter-final.
"We have to enjoy to play against the great opponent waiting for us."
Chelsea are joined in the semi-finals by Real Madrid after they overcame a scare in Germany to sneak past Borussia Dortmund.
A clash with the Madrid giants would set up a fascinating clash with the club Mourinho left last summer, but is not one he is particularly hoping for.
Asked if he wanted to face them, he said after a pause: "No, not really. Real Madrid, Barcelona, Atletico, Bayern, Manchester - it doesn't matter."
Mourinho's calm demeanour in the post-match press conference was a far cry from the animated character seen on the touchlines.
The Portuguese celebrated Ba's late winner by bolting down the touchlines in scenes similar to those witnessed when Porto knocked out Manchester United at Old Trafford en route to his Champions League success a decade ago.
"No, it was not to celebrate," he said with a smile. "It was to tell the players how we have to play the last 10 minutes.
"I knew at that moment they wanted to celebrate, they wanted to think the game is over.
"They forget that they had three plus another three or four minutes to play and the way we were playing we couldn't carry on winning 2-0.
"I had to go there because I knew it would be the only chance I'd have to tell Demba, Fernando [Torres] and Schurrle what we have to do in the last seven minutes.
"It was not to celebrate, but you could see that I can still run."
The only negative on the night for Chelsea was an injury to this season's star man Eden Hazard, who was forced off after 18 minutes through injury.
"When he comes off after 10 minutes, he was saying that he couldn't do it," Mourinho said.
"It is some problem with this calf. It's a muscular problem and, even when they are not serious, you cannot normally play for a couple of weeks, minimum.
"But I have no idea the dimension of his injury."
While Chelsea booked their place in a seventh semi-final in 11 campaigns, PSG failed to make it past the last-eight juncture for the second season in a row.
"There were a number of things that didn't work and some things did," manager Laurent Blanc said.
"We started the game better than we did in the first leg in Paris and managed the first 25 minutes before conceding when we least expected it and that gave Chelsea belief.
"In the second half Chelsea were better and we lacked fluidity, but I think we might have scored on the counter.
"Ultimately, Chelsea believed right to the end and were rewarded and good luck to them."