With the scores already locked at 1-1 from last week's first leg, goals either side of half-time from Didier Drogba and Fernando Torres took the second leg to extra time.
Michael Essien had a goal contentiously disallowed for the hosts, before Frank Lampard put Chelsea ahead from the penalty spot.
The tie was seemingly put to bed when Drogba lashed in a second from Nicolas Anelka's pull-back, but Liverpool substitute Ryan Babel struck from long range.
Chelsea saw out a nervous few minutes, though, to advance 4-3 on aggregate and ensure that they and United will now do battle over the coming three weeks for both the Premier League and Champions League trophies.
manutd.com
