After a goalless first leg at Stamford Bridge a fortnight ago, José Mourinho's Premiership leaders moved in front in the 29th minute. English international midfield player Frank Lampard gave Chelsea the lead with an angled drive into the corner of the net, rounding off a fine move involving Arjen Robben and Didier Drogba.
The home side stepped up the pressure in the second half and drew level seven minutes past the hour, Ryan Giggs getting in behind the Chelsea defence and producing a sublime finish to flick a long ball over goalkeeper Petr Cech from ten metres.
However, the visitors clinched their place in the final five minutes from time as Duff's free-kick from near the touchline evaded the entire United defence and all the Chelsea attackers before ending up in the net. At Cardiff's Millennium stadium on 27 February, Chelsea will face Liverpool FC, who defeated Watford FC 2-0 on aggregate in the other semi-final.