The Welsh side broke the deadlock in the 63rd minute when Mark Gower fired a shot into the bottom corner from 20 yards.
But Hull levelled seven minutes later with Corry Evans producing a 12-yard finish after good work from Jay Simpson, who moments earlier came on as a substitute.
The result left Swansea in fourth place and they are now unbeaten at home in six games while the Tigers extended their unbeaten away run to 16 matches.
Hull made a bright start and midfielder James Harper, who was passed fit having been struggling with a foot injury, blazed an early shot wide from 30 yards.
Swansea, buoyed by their 3-0 home win over second-placed Norwich on Saturday, responded but Stephen Dobbie drilled his 25-yard shot wide.
Gower, who scored a 25-yard screamer against the Canaries, tried his luck from similar range again but this time his effort cleared the crossbar.
The home side continued to press and they created another opening in the 22nd minute, Nathan Dyer this time unable to keep his drive on target before Dobbie again could not test goalkeeper Matt Duke.
Another opportunity fell to Dobbie but once more he could not call Duke into action, with Fabio Borini following suit moments later.
The same duo had further chances before the break but it was again the same outcome.
Hull had a chance themselves before the whistle with Evans firing wide from 12 yards.
Swansea finally forced Duke into a save 11 minutes into the second half with top-scorer Scott Sinclair being denied from 12 yards.
The visitors responded and Andy Dawson saw a header from 12 yards fly wide before Dyer was wayward once more for Swansea shortly afterwards from 12 yards.
Gower then put the Welsh side in front with a fine strike from 20 yards but the Tigers quickly restored parity through Evans, who also netted in the 2-1 win at Watford on Saturday.
Moments later James Chester nearly put Hull ahead but his header from Robert Koren's pass went wide.
Simpson certainly made an impact as with 13 minutes left he was denied by Swansea goalkeeper Dorus De Vries, who was making his 200th league appearance.
Another substitute, Luke Moore, almost did likewise for Swansea but he saw his 12-yard strike saved by Duke in the 83rd minute.
Hull looked then more likelier to snatch a later winner which almost came but once again De Vries came to his side's rescue as he foiled Matt Fryatt with two minutes left.
Moore then nearly won it for Swansea in injury time but his header drifted wide.