The Swans named an unchanged side, with manager Brendan Rodgers naming the same starting XI and substitutes that played so well to beat Norwich 3-0 on Saturday.
Hull made just one change with Matt Duke returning in goal in place of Brad Guzan who returned to Aston Villa following his loan spell. Mark Oxley was fit to provide goalkeeping cover on the bench.
James Harper and Aaron Mclean were both fit to play despite picking up knocks at the weekend.
Swansea City:Dorus de Vries, Angel Rangel, Neil Taylor, Garry Monk (c), Ashley Williams, Joe Allen, Mark Gower, Stephen Dobbie, Nathan Dyer, Scott Sinclair, Fabio Borini. Subs: Alan Tate, Darren Pratley, Craig Beattie, Luke Moore, Yves Ma-Kalambay, Tamas Priskin, Leon Britton.
Hull City: Matt Duke, Andy Dawson (c), Jack Hobbs, James Harper, Matty Fryatt, James Chester, Robert Koren, Anthony Gerrard, Corry Evans, Liam Rosenior, Aaron McClean. Subs: Mark Oxley, Richard Garcia, Tom Cairney, Jamie Devitt, Jay Simpson, David Amoo, Tijani Belaid.
Ref: R J Booth
There was a scrappy start to the game as both sides tried to gain control. In fact, it took 14 minutes for the first chance to fall to Hull when Anthony Gerrard glanced a header just wide.
Swansea slowly started to get their passing game together though as Angel Rangel was fouled 22 yards out. Mark Gower delivered it, but Ashley Williams' header was cleared with 17 minutes gone.
Their best chance came four minutes later though as good build up play between Neil Taylor and Stephen Dobbie put Rangel in overlapping wide on the ride. He drilled in a low cross, but Hull cleared the danger as Nathan Dyer prepared to pounce.
Dyer cut in from the right moments later to fire over from the edge of the area as the Swans started to step it up a gear.
And it was some neat skill from Dyer that brought the first booking of the game in the 24th minute when he was brought crashing down by skipper Andy Dawson.
Dobbie was getting in on the act as well as he weaved his way through the middle to fire a great strike that flew inches the wrong side of the post in the 29th minute.
Fabio Borini came even closer two minutes later as he latched on to a fine through ball from Dobbie. But again his shot flew inches wide.
Swansea were applying plenty of pressure now as Taylor's cross fell to Dobbie inside the area. But the midfielder fired wide.
Hull's best chance came in the 40th minute when Corry Evans fired wide from the edge of the area.
Half-time: Swans 0 Hull 0
Hull made a change at the start of the second-half with Richard Garcia coming on for Aaron McLean.
It took the Swans five minutes to get into their stride
With the first opening coming after 55 minutes when a great pass from Gower found Rangel wide on the right. He worked a neat one-two with Dobbie whose cross was deflected goalward only for James Chester to clear off the line as Sinclair looked to apply the final touch.
Swansea's second chance of the half came when Borini played in Dyer, but the winger fired wide in the 62nd minute.
But the breakthrough finally came a minute later when Taylor found Mark Gower and the midfielder created space for himself before firing a superb finish beyond Duke for his second goal in as many games.
Hull sent on Jay Simpson in the 68th minute as they went in search of the equaliser and he made an immediate impact.
Swansea only half cleared a Simpson cross and Corry Evans was perfectly placed to fire home from just inside the area for the equaliser with 70 minutes gone.
Simpson could have even put the visitors ahead a minute later as he fired just wide after Sinclair gave the ball away.
Then Chester headed a corner inches wide as Swansea were all at sea.
And it took a superb save from Dorus de Vries to keep the Swans in it as Robert Koren beat the offside trap and raced clear on goal. But with just the keeper to beat, de Vries got down well to push the ball away.
The Swans settled down to apply some late pressure as substitute Luke Moore forced a fine save out of Duke, but it wasn't Swansea's night.