Now it is Chelsea F.C. joining European football's elite in the last four for the seventh time in 11 years.
Ba seemed the most improbable player to complete Chelsea F.C.'s comeback, having been largely overlooked by Jose Mourinho for much of this season, but he delivered from the bench when it mattered most for the 2012 European champions.
Ba's sixth goal of the season in the 87th minute, after Andre Schuerrle's first-half opener, clinched a 2-0 victory that overturned a 3-1 loss from the first leg and sent Chelsea F.C. through on away goals.
"It happened so quickly,'' Ba said. "I was on the floor, just looked at the goal, and I saw the ball was in the net. It was a big joy for everyone. I just do what I have to do when I get chances. I haven't had many this season.''
Mourinho was elated, sprinting from the bench to join his celebrating players, who collapsed in a heap on the pitch.
"It was not to celebrate - it was to tell the players how we have to play,'' Mourinho said. "But you could see that I can still run.''
And Mourinho is still a winner - a decade after the Portuguese's memorable dash down the Old Trafford touchline in a game against Manchester United during his Porto side's run to the Champions League title.
Now Mourinho, having failed to bring the European Cup to Chelsea F.C. during his 2004-07 stint in charge, remains on course to win the competition in his first season back at Stamford Bridge, while the team is also second in the Premier League.
Joining Chelsea F.C. in draw on Friday is Real Madrid, which lost 2-0 at Borussia Dortmund but still went through 3-2 on aggregate. On Wednesday, Bayern Munich hosts Manchester United, and Barcelona takes on Atletico Madrid after both first legs ended 1-1.
For PSG's Qatari owners it's another season of heartbreak in Europe - a victim of the away-goals rule in the quarterfinals just as the team was against Barcelona last year - but the French title is close to be successfully defended.
This was a night when PSG needed Zlatan Ibrahimovic, but he was injured in the first leg. Edinson Cavani was relied on for goals but fluffed his chances as Chelsea F.C. extended its run without conceding at fortress Stamford Bridge to nine games in all competitions.
In a lively start, a menacing cross from Maxwell was sent to the feet of Cavani, but Petr Cech saved at the striker's feet.
What seemed to be an early setback for Chelsea F.C. proved fortuitous, with Schuerrle replacing the injured Eden Hazard after just 18 minutes and scoring in the 32nd.
Branislav Ivanovic launched the ball in from the right, and it was flicked on by David Luiz. Left completely unmarked, Schuerrle had the time and space to calmly dispatch the ball into the net.
Until that point, goalkeeper Salvatore Sirigu had only had two serious saves to make, from Frank Lampard's free kick and Luiz's long-range strike.
But, even though Chelsea F.C.'s play was far from incisive or flowing, now the hosts had hope.
The crossbar thwarted them twice within two minutes at the start of the second half: first from Schuerrle's curling shot and then from Oscar's free kick.
Mourinho beefed up the strike force in the 66th, bringing Ba on to support the ineffective Samuel Eto'o up front.
PSG's progress could have been sealed in the 78th when Yohan Cabaye launched the ball forward to Cavani, who missed the target with only Cech to beat.
"We had the chance to score and we didn't, so we paid the price for it,'' PSG midfielder Blaise Matuidi said.
With 10 minutes left to keep Chelsea F.C. in Europe, Mourinho brought on the third member of his strike force, with out-of-favor Fernando Torres replacing Oscar. Soon, the strikers that Mourinho had criticized in recent weeks were celebrating.
An initial shot by Eto'o ricocheted to Cesar Azipilicueta. The defender's shot found its way through the visiting defense, and Ba beat Maxwell to the ball - sweeping it past Sirigu with a left-footed shot from the top of the six-yard box.
"In the second half, Chelsea F.C. was a lot better and we lacked a bit of fluidity,'' PSG manager Laurent Blanc said. "But Chelsea F.C. believed until the end and they were rewarded.''