United, Barca advance
Chelsea dominated the first half at Old Trafford but Javier Hernandez's goal on the stroke of half-time put Manchester United 2-1 up on aggregate.
Wayne Rooney, who scored the only goal at Stamford Bridge last week, congratulates his Mexican strike partner.
United's 37-year-old veteran Ryan Giggs was the creator for his 22-year-old team-mate.
Fernando Torres must be slowly forgetting what it feels like to score a goal. The misfiring striker failed to find the net again and was subbed at half-time.
Chelsea's uphill task was made steeper by Ramires' second-half dismissal, the Brazilian receiving a second yellow for a needless foul on Nani.
Didier Drogba came off the bench to breathe some life into the tie, but with Chelsea needing just a goal to progress, they blew it.
Less than a minute after Drogba's equaliser, Ji-Sung Park put United two goals clear on aggregate and nipped the Blues' fightback in the bud.
Frank Lampard and John Terry stood dejected as Chelsea's Champions League dream was ended for another season.
Shakhtar Donetsk fans enthusiastically cheer on their side, who were in need of a miracle to overturn a 5-1 deficit against Barcelona.
There was to be no fairytale for Shakhtar, with Lionel Messi handing Barca a 1-0 win on the night and 6-1 aggregate victory.
Lionel Messi handed the Catalans a 1-0 victory in the Ukraine, with his 48th goal of the season beating Ronaldo's previous record of 47 for Barca in 1996-97.
Barca coach Pep Guardiola has now led Barcelona to three successive Champions League semi-finals, where Real Madrid will likely provide the oppositon.