Terry was playing for the first time since the Football Association opened their disciplinary hearing into charges the defender aimed racist comments at Ferdinand during a Premier League match last October.
The 31-year-old spent the morning at Wembley, where the FA are holding their hearing, and then dashed across London in time to link up with his teammates for the League Cup tie.
Terry, who on Sunday retired from England duty in protest at the FA’s charges, was a virtual spectator as he was treated to his side's biggest win for almost 21 months thanks to goals from Gary Cahill, Ryan Bertrand, Juan Mata, Oriol Romeu, Fernando Torres and Victor Moses.
If Terry is found guilty by FA’s independent panel, he is likely to be hit with a four-match ban.
But Terry, cleared of the same racist allegations during a court case earlier this year, received a warm welcome from Chelsea fans, who cheered his every touch.
Meanwhile, at Leeds, Everton crashed out of the League Cup after a shock 2-1 defeat against Leeds in the third round on Tuesday. The Toffees made a fine start to the EPL season and sit third in the table after Saturday’s 3-0 win at Swansea, but boss David Moyes made six changes at Elland Road and his reserves were no match for the rampant Leeds.