Gary Taylor-Fletcher grabbed a late winner to take Peter Jackson's Huddersfield side halfway to Cardiff after a thrilling Yorkshire derby at Barnsley.
Andy Booth crossed from the left five minutes from the end and as keeper Nick Colgan collided with Paul Heckingbottom, the Town winger rammed home a low shot.
But either side could have edged in front after carving out chance after chance in a nailbiting tussle that had the brought a standing ovation from the 16,000 crowd.
A goal four minutes from time by Sam Ricketts saved Swansea City and set up an exciting second-leg against Brentford at Griffin Park.
The Bees went ahead on the half-hour when Jay Tabb slid the ball home, but they went down to ten men early in the second half when keeper Stuart Nelson was shown a red card.
The Bees took the lead in the 29th minute with a goal created and finished by Tabb. He took the ball down the left flank before crossing and then the Swans defence failed to clear the ball and Tabb neatly fired the loose ball into the corner of the net.
After 52 minutes Swansea were thrown a lifeline when Nelson upended Leon Knight just outside the area and was sent off by referee Keith Stroud.
The Swans were now well on top and replacement keeper Ademola Bankole had to tip away a vicious shot from Knight.
The equaliser came after 86 minutes when Ricketts cut inside and rifled in a shot into the corner of the net, with the aid of a slight deflection.
It was what the Swans deserved as they had been on the attack for the entire second half, but though they peppered the Brentford goal in the remaining minutes they were unable to snatch victory.