The £500,000 signing from Union Berlin struck just before the interval after Rochdale had missed two glorious opportunities to go ahead. Izzy Brown hit the second from Town’s first penalty award in 10 months and half-time substitute Michael Hefele made it game over with a late double.
Huddersfield boss David Wagner hailed his players for overcoming an FA Cup culture shock.
Wagner admitted he had to throw his usual game-plan out of the window to counter their physical League One opponents in what he called “a proper British football match”.
Wagner said: “This was nothing to do with what we usually do - it was not the type of football match and style that I like but to be fair I loved the result.
“We said we had to be open to different circumstances and if you want to have an FA Cup run you have to overcome these kinds of circumstances, so credit to them for that.
“We completely changed the idea of our game, so we didn’t play as we normally do, but we had the right FA Cup attitude to work and fight and overcome those big hurdles.”
Wagner could hardly have been happier with 6ft 3ins striker Quaner, signed from Union Berlin last week, who made an immediate impression when he turned home a Brown cross.
Quaner impressed throughout and completed a first performance full of promise when he laid off to Hefele to slide home the Terriers’ fourth and final effort five minutes from time.
Wagner added: “I think it was a fantastic performance for his first game in difficult circumstances.
“He scored what we in Germany call the ‘tin-opener’ and he had some good moments. He gave a great assist for the fourth goal so you cannot really ask for more.”
Town were backed by around 3,500 fans at a Spotland ground where they had won six and drawn five of their previous 12 games, losing just once in 2010 and having defeated the Dale in their previous two FA Cup encounters (1988-89 and 1991-92).
Wagner made eight changes from the side that beat Ipswich Town 2-0 in their last Championship match as Quaner got the nod as Nahki Wells took a break on the bench.
Tareiq Holme-Dennis replaced rested left-back Chris Lowe and Martin Cranie, Mark Hudson, Harry Bunn and Jon Stankovic were handed rare starts along with goalkeeper Joel Coleman.
Rochdale were shorn of six regular first-teamers through injury, including goalkeeper Josh Lillis, son of former Town striker and Academy manager Mark.
The brought in two left-backs on loan in midweek in Stoke City’s Joel Taylor, 20, and Middlesbrough’s Mark Kitching, 21, who can both operate in other positions, and welcomed back Keith Keane from a ban.
Both loanees were handed places on the bench but Kitching was soon in action after Calvin Andrew departed following a clash of heads with Hudson. Kitching moved into central midfield as Reuben Noble-Lazarus went wide.
The latter provided the cross from which Peter Vincenti should have put the hosts ahead but he headed over from close range after an initial corner had skimmed off heads out to the left.
Ian Henderson then hit wide from outside the area as Coleman rushed out after the striker intercepted Hudson’s wayward back-pass.
It took Town until the 39th minute to test Conrad Logan, who made a smart save at the foot of his left post from Philip Billing’s low drive.
A free-kick from the left was missed by Vincenti, allowing Hudson to strike a half-volley narrowly over before Town took a 42nd-minute lead.
The ball was switched out wide to Bunn, who sent Izzy Brown down the left channel to slip the ball across to Quaner for a simple tap-in.
Town made two changes at the break, Jonathan Hogg replacing Bunn and central defender Hefele being brought on up front for Elias Kachunga - Wagner switching to a 4-3-3 formation.
Rochdale’s attempts to hit back were undone by a series of poor crosses, which Coleman easily claimed and Town made it 2-0 in the 67th minute through their first penalty since March last year.
Jimmy McNulty conceded a corner as Billing threaded the ball through, aiming for Hefele. Holmes-Dennis sent the flag kick deep and referee Oliver Langford spotted Hudson being dragged down and pointed to the spot.
Brown had no trouble sending Logan the wrong way from 12 yards.
Rochdale made their last two changes and Town brought on Aaron Mooy for Whitehead, the Australian soon supplying the free-kick from which Hefele rose the highest to plant home a downward header in the 72nd minute.
Holmes-Dennis cleared a dangerous cross but there was no way back for the Dale as Hefele struck again in the 85th minute after a diagonal ball found Quaner, who squared for his fellow German to gleefully sidefoot home.
Rochdale: Logan, Rafferty, McGahey, McNulty, Keane, Allen, Andrew, Camps, Vincenti, Noble-Lazarus, Henderson. Subs: Kitching, Taylor, Redshaw, Canavan, Mendez-Laing, McDermott, Diba Musangu.
Huddersfield: Coleman, Cranie, Hudson, Stankovic, Holmes-Dennis, Whitehead, Billing, Kachunga, Brown, Bunn, Quaner. Subs: Ward, Smith, Hogg, Mooy, van La Parra, Wells,
Referee: Oliver Langford (W Midlands)