Swindon manager Andy King saluted his side's battling performance after they booked their place in the next round to see off the challenge of Division Two rivals Huddersfield.
Captain Andy Gurney's strike six minutes from the final whistle was enough to settle a poor game and leave debt-ridden Swindon just one game away from a possible big pay- day against one of the country's glamour clubs.
Leading scorer Sam Parkin was the maker as he headed Danny Invincibile's cross into Gurneys path for the defender to fire home from six yards out.
King said, "It was a job well done and we have achieved our aim of getting into the next round.
"I said to my players at half time that one goal would be enough to win it because the game was very tight.
"It was a scrappy match with no atmosphere, but we are in the second round and I now want a home draw against someone we can beat so we stand a chance of playing one of the bigger teams." Parkin brought a good save from Town goalie Scott Bevan in the 39th minute while Invincibile should have broken the deadlock in the 68th minute, but he somehow sliced his shot wide from just four yards out.
Huddersfield have scored just 13 goals in the second division this season the lowest in their league and the lack of confidence showed as they spurned several chances which would have forced a replay.
Leading scorer Martin Smith went close on three separate occasions while Danny Schofield shot inches wide of the right-hand post when presented with a chance in the 53rd minute.
Defender Nat Brown looked to have broken the deadlock a minute later but his shot from four yards out was cleared off the line by midfielder Matt Hewlett