Graham had not found the net since leaving the Liberty Stadium earlier this year, but he returned to haunt his former club with a fine far-post finish in just the eighth minute.
The Tigers kept their hosts at bay with ease until the hour mark when Jonjo Shelvey’s driven ball from a short corner hit Chico Flores and flew in to give the Spaniard his first Premier League goal, although replays suggested the ball had come off his arm on the way into the net.
Hull could still have won it had referee Martin Atkinson not missed a blatant handball by Swansea defender Dwight Tiendalli as he blocked an Alex Bruce header.
Much had been made of Graham’s return to Swansea and a goal drought stretching back to January 9.
It was almost inevitable he would end it against his former club, and so it proved.
A poor Ashley Williams pass was picked off by Ahmed Elmohamady and his fine deep cross was converted at the back post to give Graham his first top-flight goal in 1,626 minutes.
Swansea, with Michu back in action after five weeks out, had started positively as they looked to pick up where they had left off against Newcastle last week.
Twice Pablo Hernandez found space in front of the Hull defence, finding Nathan Dyer, who curled wide, and then failing to locate Michu.
But they fell behind in the eighth minute as Graham ended his 11-month wait for a goal with his calm, far-post finish which, despite the relief he must have felt, he barely celebrated in a nod to the home support.
Swansea continued to have stacks of possession, but it counted for very little as they struggled to break down their visitors.
Hull were well-organised, compact, and deprived their hosts of space in between defence and midfield, where they can thrive if given the chance.
Home frustrations steadily grew, as did the scrappiness in Swansea’s play.
They did work a half chance for Jonathan de Guzman, but he blazed miles over the bar.
Swansea were booed off at the break, but there was little improvement after the interval and Tom Huddlestone, who picked off countless stray Swansea passes, could have doubled their lead only to prod over a loose ball from the edge of the box.
It took the introduction of Alejandro Pozuelo in the 58th minute to spark some urgency into Swansea’s play and the equaliser quickly arrived, although in dubious circumstances, through Flores.
Hull responded strongly and pushed Swansea back but they were on the wrong end of a second contentious handball decision with 20 minutes remaining after Tiendalli used both his hands to make his block.
David Meyler thought he had put them back in front as they continued to press, but had strayed just offside as he ran on to meet Jake Livermore’s header.
Yannick Sagbo then stung Gerhard Tremmel’s palms with a fierce drive from distance.
Michu worked Allan McGregor at the other end before Williams and Sagbo were booked after an unseemly squabble before Flores, himself on a booking, flung himself to the ground feigning that Sagbo had elbowed him.
It proved the last meaningful effort as Hull held off a late Swansea flurry without alarm.