The Swans rose to the top of half of the table after Chico Flores' second-half equaliser earned them a point against Hull City at the Liberty.
Danny Graham edged the visitors in front against his former club as he scored his first goal in 11 months after volleying home Ahmed Elmohamady's cross in the ninth minute.
Graham, on loan from Sunderland, didn't celebrate as he found the net for the first time since scoring for the Swans in their Capital One Cup win at Chelsea last January.
The visitors, a well-organised side, frustrated the Swans and held out comfortably until the break.
But after a series of attacks, the Swans got their equaliser on the hour mark as a quickly-taken corner allowed Jonjo Shelvey to fire in a delivery which Chico steered home.
Hull then had a strong penalty appeal, which was turned down, and then David Meyler saw his goal disallowed for offside.
Both sides, though, had to settle for a draw which meant the Swans moved onto 19 points from 15 games and up to tenth spot.
The Swans made three changes to their starting XI.
Michu returned from the ankle injury which had ruled him out since the derby defeat at Cardiff last month while Gerhard Tremmel started in goal in place of Michel Vorm, who had a knee problem.
The final change saw Nathan Dyer - a goalscorer in the 3-0 win over Newcastle last time out - start as Alejandro Pozuelo was back among the substitutes.
Hull boss Steve Bruce made just one change as he named skipper Curtis Davies in his line-up after he missed the midweek defeat at Arsenal while Danny Graham - on loan from Sunderland - returned to the Liberty Stadium to face his former club.
SWANS:Gerhard Tremmel, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies, Jose Canas, Jonathan de Guzman (Alejandro Pozuelo, 56), Jonjo Shelvey, Nathan Dyer, Pablo Hernandez (Wayne Routledge, 67), Michu.
SUBS: Gregor Zabret, Jordi Amat, Neil Taylor, Roland Lamah, Rory Donnelly.
HULL:Allan McGregor, Maynor Figueroa, Alex Bruce, James Chester, Curtis Davies (capt), David Meyler, Tom Huddlestone, Danny Graham (Robert Koren, 64), Jake Livermore, Yannick Sagbo, Ahmed Elmohamady.
SUBS: Steve Harper, Leroy Rosenior, Robbie Brady, Paul McShane, George Boyd, Abdoulaye Faye.
Prior to kick-off, members from the 2003 Swans side that ensured the club retained its Football League status with that famous win over Hull on the final day of the season were introduced onto the pitch.
The home crowd were up on their feet, applauding the efforts of those players who played such an important part in the club's rise from the bottom of the Football League to the top division in the English pyramid.
The Liberty Stadium also paid tribute to Nelson Mandela, with one minute's applause for the former South Africa president who passed last week.
The Swans got off to a decent start on a cold night, with Michu slipping through a pass for Nathan Dyer, but when the winger cut back inside onto his right foot he could only curl his shot high and wide after three minutes.
Pablo Hernandez was the next to benefit from an excellent pass as the Spaniard raced on into the box, but he couldn't find his countryman with the return pass.
Then, with Hull's first attack, the visitors stunned the Liberty by taking the lead in the ninth minute.
After Ashley Williams' pass was intercepted by Ahmed Elmohamady, the latter raced on and rode Hernandez's sliding challenge before his curling cross was volleyed home by Danny Graham past Gerhard Tremmel.
The striker, finding the net for the first time in 11 months, didn't celebrate in front of the Swans fans as a show of respect for his former club.
The Swans found it hard to get going against the Tigers, and it wasn't until before half-hour mark that they threatened next as Michu's neat back-heel teed up Ben Davies, but he fired just over from 20 yards.
Hull were well organised and made it difficult for the Swans to break through.
A Jonathan de Guzman effort from 25 yards was all the home side could muster from a period of possession, but that flew well over the crossbar with Allan McGregor untroubled as the half came to a close.
HALF-TIME: Swans 0 Hull 1
The Swans went looking for a leveller early in the second half, but it was Hull who created the first chance after the restart as Tom Huddlestone volleyed high into the away supporters from an Elmohamady cross.
Michael Laudrup then made his first change after 56 minutes as Alejandro Pozuelo came on for de Guzman.
And minutes later the Swans were level as, following a quickly taken corner, Jonjo Shelvey's thunderous delivery was turned in by Chico Flores from six yards out.
Hull boss Steve Bruce then made a change as Graham was replaced by Robert Koren, with Laudrup also sending on Wayne Routledge for Hernandez.
The visitors then had the ball in the net as David Meyler latched onto a ball over the top of the defence, but when he slotted into the bottom corner the assistant referee's flag was raised.
They pushed again, and the ever dangerous Yannick Sagbo drove a thunderous half-volley which Tremmel parried wide while at full stretch.
Then, at the other end, sub Routledge sent Michu through with a neat backheel, but the Spaniard's effort was saved by the legs of Allan McGregor.
The Swans pushed hard for a winner, but Hull's stern backline held out for a point.