Eidur Gudjohnsen rescued Chelsea with a late winner after Huddersfield had briefly threatened to pull off one of the biggest FA Cup shocks in recent history.
England Under-21s international Carlton Cole, making his first start of the season, put Chelsea in front in the 12th minute when he converted Damien Duff's low cross at the second attempt.
But Gary Taylor-Fletcher stunned the Barclays Premiership champions with a second-half equaliser, before Gudjohnsen put them into the next round by supplying the the finish to Arjen Robben's left-wing cross nine minutes from time.
It was no surprise when the champions took the lead through Cole.
The striker collected a low cross from Damien Duff - and after his initial effort was half-blocked by Martin McIntosh, the 22-year-old quickly recovered to head the loose ball beyond Town goalkeeper Phillip Senior.
In the 71st minute, Robben replaced Duff as Mourinho looked for the second goal.
Chelsea paid the price for their woeful finishing in the 74th minute when Michael Collins fed Taylor-Fletcher, and the former Lincoln striker beat Carlo Cudicini with a low drive to put the minnows level.
But nine minutes from time, Gudjohnsen sank Town's hopes of earning themselves a replay when he finished off a great run and cross by Robben.
