Henderson, a £2million summer signing from Watford, capitalised on some slack defending to equalise with eight minutes remaining after Huddersfield had taken the league courtesy of a first-half strike by Michael Flynn.
And just 60 seconds after levelling the contest, Henderson fed substitute Kyle Naughton who unleashed a ferocious shot from the edge of the area that took a slight deflection off Huddersfield's Robbie Williams.
It was the hosts that had started the better, with winger Gary Roberts having a header well saved by the Blades' star player Ian Bennett.
Town should have gone ahead in the 20th minutes through Nathan Clarke, but the centre-half guided his header inches wide.
However, Huddersfield's pressure eventually paid dividends as Flynn broke the deadlock in the 34th minute.
Flynn, who was one of ten new players bought by Town boss Stan Ternent during the summer, curled home a sublime 25-yard effort after a quick free-kick from Roberts.
The Terriers pushed for the decisive second goal after the interval, and only a smart stop from Bennett stopped Roberts increasing their advantage.
Moments later, a neat turn by Keigan Parker gave the striker a sight of goal but his drive from distance was gathered by Bennett.
However the visitors hit back, and a cross-cum-shot by Matthew Kilgallon with 15 minutes remaining flew inches over the top to the relief of the home faithful.
However, the Blades ended the game strongly to earn their place in the third round with two late goals in 60 seconds.