It was a miserable day for Fulham's Clint Dempsey as the hosts grabbed a crucial three points at the Liberty Stadium.
United States international Dempsey had been unfortunate to get in the way of Scott Sinclair's 56th minute strike and deflect the ball beyond Fulham keeper Mark Schwarzer to give Swansea the lead.
Fulham, without striker Bobby Zamora who was rested amid speculation of a falling out with manager Martin Jol, looked set to level when Jazz Richards was adjudged to have brought down Karim Frei with just four minutes to go but Vorm athletically denied Dempsey's spot-kick, before substitute Graham slid home the clincher in stoppage time to secure three vital points.
Swansea boss Brendan Rodgers had brought defender Steven Caulker into his side along with Luke Moore and Wayne Routledge, and the latter pair were at the centre of most of Swansea's promising attacking moments during a first half they dominated without ever really threatening Schwarzer's goal.
Sinclair was just unable to get a shot away after linking with Leroy Lita, before the striker headed wide from a Routledge cross in a bright opening.
The Cottagers enjoyed a rare forward foray as Richards denied Andrew Johnson after the striker had got the better of Caulker on the left side of the box, but the action was quickly back at the other end as Moore went closest to a goal during the opening period when he flicked the top of the bar with a superb, swerving strike from just outside the box.
Fulham survived two penalty appeals against John Arne Riise after the Norway international was fortuitously awarded a free-kick after appearing to haul down Lita, before he was adjudged not to have handled a Routledge cross, but they remained largely untroubled despite having only scraps of possession.
Schwarzer made the first save of the afternoon after half an hour when he held a low Sinclair shot, although the visitors did alleviate the pressure long enough for Dempsey to head wide with their first genuine effort on goal.
Schwarzer required treatment early in the second half after suffering a heavy landing when falling over Lita whilst claiming a high ball, but was fit to continue.
The home crowd's frustrations were beginning to grow but a game that had hardly made for absorbing viewing sprang to life when Swansea's persistence was finally rewarded.
Schwarzer's punch only went as far as Routledge, his scuffed effort was turned goalward by Sinclair and a huge deflection off the unfortunate Dempsey left his keeper stranded and gave the Swansea man his first goal from open play this term.
Fulham responded but Vorm, who had been almost a spectator up to that point, made a superb low save to deny Bryan Ruiz from eight yards, before holding an angled drive as Dempsey sought to make amends for his ill fortune.
It was suddenly all Fulham as Riise fizzed a free-kick just wide and Vorm raced out to deny Johnson.
But with Fulham searching for an equaliser a rapid Swansea break almost saw them double their lead.
Sinclair teased full-back Stephen Kelly before teeing up substitute Kemy Agustien, whose side-footed effort beat Schwarzer but struck the post barely a minute after he had taken the field.
Frei then went tumbling over Richards in the box and referee Jon Moss pointed to the spot, only for Vorm to make a stunning stop to his right to deny Dempsey, before Graham grabbed his fifth goal of the season from Gower's corner in added time to seal the victory.