(CNN)Thiago Silva's path to redemption took a mere 12 minutes. For that short period of time the Brazilian must have been panicking that his needless error had cost his Paris Saint-Germain side a place in the last eight of the European Champions League. His handball had gifted English Premier League leaders Chelsea a 2-1 aggregate advantage in extra time, but this was one tale that would be adorned with a Silva lining. Seconds after being denied by a world class save from Thibaut Courtois, Silva looped a header into the net to send PSG through on away goals. Not only did he save himself from a barrage of criticism, he also got colleague Zlatan Ibrahimovic out of jail too. The maverick Swedish striker's dismissal after 31 minutes made PSG's passage into the quarterfinals all the more remarkable, as it battled the best team in England with 10 men for an energy-sapping 90 minutes. Gary Cahill looked to have ended PSG's resistance with a 81st minute goal before former Chelsea defender David Luiz equalized with four minutes left. Eden Hazard converted from the spot in extra time after Silva's misdemeanor before the 30-year-old popped up at the death to make amends and avenge PSG's defeat at the same stage by Chelsea last season. "We played a great game," Luiz told Sky Sports. "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. "It's amazing for the club and the city. We tried to win the game even with one less man. We have a long way to go to win the Champions League and we keep our feet on the floor." The first tie ended 1-1 in Paris three weeks ago but most of the headlines related to an ugly incident of racism on the city's Metro system. A group of supporters, apparently Chelsea fans, were caught on camera appearing to prevent a black man from boarding a train before chanting: "We're racist and that's the way we like it." The UK's Metropolitan Police announced on Wednesday that it had summoned five men to appear in court later in March, while Chelsea has vowed to ban for life any of its fans that are found guilty. The club extended an invitation to the man who was the the subject of the abuse, known as Souleymane S, but the 33-year-old refused. The opening stages were tense and feisty, just as they were in the French capital during the first leg, but the match in London ignited after a flashpoint just past the half hour mark. Ibrahimovic, so often the hero for PSG, turned villain after being dismissed for a forceful tackle on Chelsea's Brazilian playmaker Oscar. The home side surrounded referee Bjorn Kuipers who duly produced a red card -- the fourth of the Swede's often controversial career in the Champions League. But replays suggested the 33-year-old was perhaps unfortunate to see red, having tried to pull out of the tackle at the last second. Despite having a man advantage, Chelsea struggled to create clear cut openings as PSG defended resolutely. Kuipers was in the spotlight again as the half came to a close -- a mazy run from striker Diego Costa ended when he was felled by PSG's Uruguayan forward Edinson Cavani. The referee took a long look at the incident but decided to wave play on, much to the chagrin of Chelsea's players and manager Jose Mourinho. Mourinho's travails continued after the break as the Blues toiled in its attempts to open up a determined PSG rearguard. A half chance for Gary Cahill came and went before the visitors came to the fore. First Cavani played in Maxwell, whose ball across the face of goal was begging to be tapped in, before the Uruguayan had a chance to tilt the tie firmly in his side's favor. Played in on goal by Argentinian Javier Pastore, Cavani rounded Chelsea goalkeeper Thibaut Courtois but could only glance a shot off the near post from a tight angle. Pastore then got into the area after neat approach play and, though he got a powerful low shot away, Courtois was equal to it and palmed it clear. Chelsea began to reassert its dominance as PSG tired. Substitute Ramires weaved into the area and was denied by a fine save at his near post by Salvatore Sirigu. From the resulting corner a miskick from Costa presented the ball at the feet of England defender Cahill, who lashed home from 12 yards out. But Chelsea were unable to hold out. Luiz, who won the Champions League with Chelsea during a three-year stint at the club, had been booed throughout the game for a running battle with Costa. And he rose highest to power a header into the net and make the tie level on aggregate with just four minutes remaining. PSG began the extra half hour in sluggish fashion and were punished when Silva needlessly handled a looping cross into the area as he went up to challenge substitute Kurt Zouma for the ball. Belgium international Eden Hazard duly tucked the penalty away, to restore Chelsea's lead and ensure the tie would not go to penalties. Still Chelsea looked edgy. Courtois was forced to make a world class save from Silva, as the Brazilian desperately tried to make amends for his handball. But despite that warning, Silva netted with a fine header from the very next corner, looping a brilliant header over the goalkeeper from 14 yards out. After the game Mourinho admitted PSG had "clearly" been the better side: "Our performance was not good enough," he told Sky Sports. "We had the game in our hands twice but I think PSG were stronger than us and coped better with the pressure of the game." German champions Bayern Munich cemented its place in the last eight with a comprehensive 7-0 dismantling of Shakhtar Donetsk. After a 0-0 draw in the first leg in Ukraine, Shakhtar's task became an uphill one inside four minutes when Olexandr Kucher was dismissed for bringing down Mario Götze inside the penalty area. Thomas Muller tucked home the resulting penalty, and Bayern subsequently laid siege to Shakhtar's goal. Robert Lewandowski nodded Rafinha's cross against the post before Pep Guardiola's side doubled its advantage just after the half hour mark. Defender Jerome Boateng had the simple task of tapping home from point blank range after former Dortmund striker Lewandowski's effort had been saved. Bayern ran riot after the break, France international Franck Ribery grabbing the third with a fine low finish after a powerful run into the area. Muller grabbed a second moments later before Holger Badstuber made it five with a thumping header. Lewandowski finally got on the score sheet before Götze completed the rout.
French side Paris Saint-Germain knock Chelsea out of the European Champions League . A goal in extra time from Thiago Silva sends French champions through on away goals . PSG played 90 minutes with 10 men after Zlatan Ibrahimovic's first-half dismissal . Bayern Munich hammer Shakhtar Donetsk 7-0 to book its place in the last eight .