Debutant goalkeeper made two saves in the penalty shoot-out as the visitors came through 4-2 but it should not have come to that.
The Owls needed to produce four outstanding pieces of defending for the game to finish 0-0 after 90 minutes, although Jordan Rhodes missing a very late headed chance on his quick return to Hillsborough was important too.
For a Huddersfield side who produced dreadful cup surrenders in Carlos Coerban's first season of English cup football, it was a welcome win but Darren Moore could at least take satisfaction from the insatiable hunger Barry Bannan showed for keeping a clean sheet.
There will have been plenty of Owls fans worried they would lose their Championship-quality cultured midfielder once the team dropped out of the second tier but when the Scot says he is committed to this club, it is more than just words.
The four highlights of the 90 minutes were brilliant bits of defending and Bannan played a part in three.
Bannan produced a lung-busting run to track back, albeit it nearly cost his side because when he gave it to Sam Hutchinson, the centre-back twisted and turned looking for a chink of light to thread the ball through rather than wellying it into row Z. Duane Holmes showed good footwork from the resulting corner, but chipped wide.
When Holmes forced Bailey Peacock-Farrell to save in the 67th minute, Thomas's eyes must have lit up as the rebound fell to him, only for Hunt to make a brilliant tackle.
Bannan was instantly over with a Bonucci-style celebration for the defending.
Then, best of all, the captain chased Thomas back as he went through on goal and produced a wonderfully-timed lunge of a tackle which won the ball cleanly, had him down on the turf injured, and earned huge applause when he got to his feet and played on. When Bannan made way with six minutes to go, he got his first ovation after 15 crowd-free months and it was richly deserved.
The last heroics were Sam Hutchinson's in stoppage time, knocking a goalbound Rhodes header behind for a corner. When the ball came back in again a minute later there were no excuses for the former Owl not burying his header. At least he put his penalty away.
Where for over a year the players have emerged from the tunnel to Simple Minds echoing around, this tme they had the added soundtrack of around 12,000 roaring fans spread around three stands.
It instantly made for a better game, if not a classic.
Huddersfield set out in a 4-3-3, Wednesday more of a 4-2-3-1 with greater freedom for Lewis Wing. The Owls had five full debutants to the Terriers' four. Jaden Brown and Rhodes, who swapped sides over the summer, were on the bench, though Brown came off it earlier than expected, Rhodes not until the final 10 minutes.
As befitting the fact Town are now the higher-division side, it was home goalkeeper Peacock-Farrell who was the busier goalkeeper in the first half.
He made his first save in the 13th minute when the lively but raw Owls midfielder Dennis Adeniran was caught in oissession and good work by Danny Ward and Josh Koroma played Scott High in for a shot beaten away.
He would end the half with a save from Josh Koroma, cutting in off the left.
Andre Green's unwise pass across his defence almost set up a Huddersfueld attack but when Danny Ward was unable to control it showed the other side of how Moore wants his side to play, Hutchinson bursting out of defence. Although Olamide Shodipo's cross was cut out, it lifted the home fans.
Fellow centre-back Dominic Iorfa also galloped out from the back later in the half, though all it got him was a booking when he fouled O'Brien, closing him down.
O'Brien showed why Leeds United are reportedly so keen on him, and why it will be expensive to sign him. An early diving header was miles off target but it was the positive running which was impressive, as was a tackle on Adeniran a minute later. He was at the heart of most of his side's best football.
He forced a low save after robbing Adeniran, who quickly responded with a saved shot of his own.
When Wing, on loan from Middlesbrough, produced an excellent sweeping ball to release Shodipo, the winger broke down as well as the move, with what looked like a hamstring strain. It meant Brown's first competitive outing for the Owls was as a left winger.
The second half was just as lively, Brown hitting a shot into the side netting and forcing Nicholls into a rare save that would warm him up for what was to come.
The score was 2-2 after four kicks, Hutchinson, Adeniran, Rhodes and Thomas all converting, when Nicholls denied the unconvincing Massimo Luongo and Liam Palmer.
Harry Toffolo and Lewis O'Brien converted to send their team through.
Sheffield Wednesday: Peacock-Farrell; J Hunt, Iorfa, Hutchinson, Palmer; Adeniran, Bannan (Luongo 84); Green (Dele-Bashiru 75), Wing, Paterson, Shodipo (Brown 34).
Unused substitutes: Adedoyin, Dunkley, Wildsmith, A Hunt.
Huddersfield Town: Nicholls; Turton, Pearson, Colwill, Toffolo; High (Sinani 89), Hogg, O'Brien; Holmes, Ward (Rhodes 81), Koroma (Thomas 58).
Nout used: Vallejo, Ruffels, Sarr, Schofield.
Referee: D Bond (Lancashire).