Poor clearing
Arsenal took the lead at Anfield when Abou Diaby scored from a tight angle in the 13th minute after some poor clearing shots by the Liverpool defence.
Sami Hyypia then equalised for Liverpool in the 30th by getting away from Philippe Senderos and heading in a corner from Gerrard. Fernando Torres put the hosts ahead in the 69th by controlling a long pass from goalkeeper Pepe Reina with his chest and turning to beat Manuel Almunia.
Emmanuel Adebayor scored an equaliser for the Gunners in the 84th after a spectacular run down the right by Theo Walcott. That would have been enough to send Arsenal through on away goals, but Gerrard scored from the spot a minute later after Kolo Toure pulled down Babel in the area.
''They held me a little bit and they tried to take a chunk of me,'' said Babel, who added to the lead in the second minute of injury time.
Arsenal manager Arsene Wenger disagreed with the penalty, and added that he thought Alexandre Hleb was denied a penalty in the first leg.
''The defeat was down to a dodgy decision of the referee I think,'' Wenger said. ''I believe over the two games it's difficult to swallow because of the double disappointment and all the big decisions were against us.''
It was the third match between Arsenal and Liverpool in seven days. Besides the two legs of the Champions League, Liverpool drew 1-1 at the Emirates Stadium in the Premier League on Saturday.
Liverpool beat Chelsea in the Champions League semi-finals in 2005 and 2007, winning their fifth title in '05.
"We've been there. We know everything about them and they know everything about us,'' Lampard said. "It's amazing how often we've been in this situation.''
Ballack gave Chelsea the lead in the fourth minute by heading in a cross from Lampard from the right. Lampard scored the second off a cross from Michael Essien in the 87th.
The result extended Chelsea's home unbeaten streak in Europe to 11, a run dating back 26 months.
Chelsea, already playing without the injured Petr Cech, were forced to replace second-string goalkeeper Carlo Cudicini in the 26th with Hilario because of injury.