* Late goal from Senegalese substitute Ba seals win
* Battling Chelsea reach last four on away-goals rule
* Stunned PSG fail to end wait for semi-final place (Adds details, quotes)
By Mike Collett
LONDON, April 8 (Reuters) - Chelsea snatched a dramatic late goal through Demba Ba to beat Paris St Germain 2-0 and reach the Champions League semi-finals on the away goals rule on another memorable European night at Stamford Bridge on Tuesday.
Substitute striker Ba, who replaced Frank Lampard midway through the second half, struck with time running out for the 2012 European champions, who looked to be going out of the competition after losing the first leg 3-1 last week.
But Ba's goal in the 87th minute levelled the tie at 3-3 and Chelsea, evoking memories of their battling and ultimately successful campaign two seasons ago, went through on away goals thanks to Eden Hazard's penalty in Paris last week.
Andre Schuerrle, who replaced the injured Hazard after only 17 minutes on Tuesday, had given Chelsea hope with a superbly taken goal after 32 minutes but Jose Mourinho's perfect record of winning all eight European quarter-finals he had been involved in, seemed about to end with time running out.
Ba sealed victory, though, when a Cesar Azpilicueta shot was deflected to him in the area and he scooped the ball past keeper Salvatore Sirigu to send the home fans into raptures as Mourinho sprinted down the touchline to join his celebrating players.
"It all happened so quick," said Ba. "I saw the ball and it was in the goal. I just do what I have to do when I get chances. I didn't have chances this season but tonight I took it."
Chelsea manager Jose Mourinho added on ITV: "Demba made a crucial finish for us and I think very much deserved. The team that decided to defend was punished and the team that played with their heart deserved to go to the semis."
The Portuguese coach's dash along the touchline evoked memories of his famous Old Trafford celebration when his Porto side beat Manchester United in 2004 although this time he was also keen to tell his players not to take any risks.
It is the seventh time in 11 Champions League campaigns that Chelsea have reached the last four and Mourinho is on course to become the first manager to win the European Cup with three clubs after triumphs with Porto in 2004 and Inter Milan in 2010.
Mourinho had told his players to "go out and play with a smiles on their faces" as they had nothing to lose after last week's defeat, but they failed to make an early impression as PSG dominated the midfield and pegged Chelsea back.
Thiago Motta, Blaise Matuidi and Marco Verratti took a stranglehold in the middle of the park for the visitors, who were playing with the kind of confidence that comes from a team who have won their last 11 matches.
But PSG coach Laurent Blanc, who said his best form of defending their first leg lead was to attack, appeared to have different tactics in reality and his side failed to seriously test Chelsea when they held the upper hand.
Although PSG were minutes away from reaching the last four for the first time since 1995, their was an increasing air of inevitability that Chelsea would steal that chance from them.
The visitors' only real attempts came in the closing stages with the score still 1-0 on the night and PSG 3-2 ahead on aggregate when striker Edinson Cavani twice went close.
If either of those efforts had gone in, Chelsea would have probably gone out but the London side survived and took their own scoring opportunity when it came.
They had also gone close twice early in the second half when first Germany international Schuerrle, who had a magnificent match, and then Oscar, from a freekick, clattered the bar.
With their fans roaring them on, Chelsea finished by far the better team and it seemed a matter of time before they repeated their heroics against Napoli in 2012.
On that occasion they came back from losing the first leg 3-1 in Italy to win 4-1 at Stamford Bridge after extra time before going on to win the trophy a few months later.
"This competition means a lot to us," said Chelsea defender and captain John Terry, who was suspended for the final when Chelsea won the competition for the only time.
"The experiences we have had keeps you fighting and believing. Winning it was the best feeling ever. These big performances are what we live for.
"Everyone doubted us tonight but we showed great character and fight to come back. It all paid off," he added on ITV ahead of Friday's semi-final draw. (Reporting by Mike Collett; Editing by Ken Ferris)