Jack Payne scored twice as Huddersfield ended a run of six cup matches without a win with a 4-0 victory over Port Vale.
Payne, signed from Southend last summer, took his tally for the season to three with the first and last goals after Kasey Palmer and Harry Bunn also found the net.
While Town's first cup win since they beat Chesterfield in the Capital One Cup in August 2014 rarely looked in doubt, it took them until the latter stages of the game to secure their place in the FA Cup fourth-round draw.
Huddersfield fielded a much-changed side but still had too much class for the managerless League One strugglers.
Town stroked the ball around and controlled possession right from the off. Playing a fluid system up front with no out-and-out striker, left-back Tareiq Holmes-Dennis found himself in the box and it took a great saving tackle from Nathan Smith to stop him.
Philip Billing, who has a reputation for spectacular long-range goals, tried his luck from outside the box but fired well over the top.
Vale goalkeeper Jak Alnwick pulled off a great save in the 22nd minute - but certainly felt it.
Palmer's corner was met by centre-back Mark Hudson and his header into the ground was heading for the top corner before Alnwick flung himself to tip over.
The keeper's momentum caused him to crash into the post and he needed treatment on the pitch before he could continue.
Alnwick showed he had suffered no ill effects four minutes later when he turned around a powerful shot from Joe Lolley.
Alnwick, however, had no answer when Town took the lead in the 28th minute. Some slick football saw debutant Izzy Brown run at the Vale defence and slip the ball through for Lolley who set up Payne to fire home off the inside of the far post.
Billing again shot from distance and Lolley took his time but was off target.
Palmer had a good chance to make it 2-0 in stoppage time when he collected a superb through ball from Jo Gorenc Stankovic but he fired over when one-on-one with Alnwick.
In the second half Lolley ballooned over and Martin Cranie's effort was ruled out for offside.
Palmer then went close before keeper Alnwick's injury became too much and he limped off in the 59th minute to be replaced by Miguel Santos.
Brown, on his debut after a loan move from Chelsea, should have scored but his shot drifted wide.
Town missed some straightforward chances but one of the harder ones was taken by Palmer to finally make it 2-0 in the 73rd minute.
Substitute Bunn was involved in the build-up but Palmer did all the work himself when his 20-yard strike took a deflection to beat Santos.
As Vale tired Town clinched the game. Tommy Smith set up Town's third in the 80th minute with a through ball for Bunn who ran forward, side-stepped a defender and gave Santos no chance.
The victory was completed when Holmes-Dennis crossed from the left for Payne to slot home unmarked with six minutes left.