Scott Sinclair scored the only goal of the game as Brendan Rodgers made a successful return to Reading.
The flying winger struck towards the end of the first-half to take his tally to nine in 10 games and help guide the Swans to a first win in Berkshire for over 25 years.
Nathan Dyer hit the bar after the re-start and Stephen Dobbie and Andrea Orlandi came close to adding a second, but they had to show nerves of steal at the back to claw out an important result.
The Swans had both Darren Pratley and Sinclair back in their ranks for the game at the Madejski Stadium.
They missed the last outing against Derby two weeks earlier but slotted straight back into the starting line-up against the Royals, replacing Joe Allen and Cedric van der Gun.
The latter dropped back down to the bench, joining David Cotterill who also returned from injury, while youngster Allen wasmissing with a groin problem.
Reading: Adam Federici; Andy Griffin, Ian Harte, Zurab Khizanishvili, Matt Mills (C); Chris Armstrong, Jem Karacan, Jimmy Kebe, Hal Robson-Kanu (Noel Hunt, 67'); Jobi McAnuff, Shane Long (Simon Church, 77').
Not Used: Michail Antonio, Brian Howard, Shaun Cummings, Alex Pearce, Alex McCarthy.
Swans:Dorus de Vries; Angel Rangel, Garry Monk(C), Ashley Williams, Alan Tate; Mark Gower (David Cotterill, 20'), Andrea Orlandi, Darren Pratley, Nathan Dyer (Albert Serran, 85'), Scott Sinclair; Stephen Dobbie (Frank Nouble, 76').
Not Used:Yves Makabu-Makalambay (GK), Neil Taylor, Craig Beattie, Cedric van der Gun.
Attendance: 18,418 Away: 2,199
Referee: O Langford (West Midlands)
The scarfs and wooly hats were out in force at the chilly Madejski Stadium to signal the start of 'that time' of the football season.
It didn't deter the near-2,000 members of the Jack Army to make the reasonably short trip along the M4 and they found their voices early on in Berkshire.
It was a first return to the club for Brendan Rodgers who was looking to mastermind a win against his former employers, just two and a bit weeks after guiding the Swans to victory at another ex-club, Watford.
The hosts started this encounter the strongest, however, looking to cause problems from two early corners, while the closest the Swans came to a first attempt fell on seven minutes when Andrea Orlandi misjudged his free-kick and found the stand.
Barely two minutes had past when Shane Long, Reading's number nine, had the home fans on their feet when he glanced Jimmy Kebe's cross over the top of goal with his head from six-yards.
The Swans were forced into making an early change as David Cotterill was introduced to replace a hobbling Mark Gower with just 20 minutes on the clock. This added an attacking edge to the formation and they went on to dominate possession for the next 10 minutes, which included a penalty shout from Nathan Dyer.
Jem Karacan did see a shot deflect wide for a corner just before the half-hour while Hal Robson-Kanu's rifled attempt also deflected over goal moments later.
But after that brief moment of Reading pressure the away side silenced the Royals' faithful with an opener - Ashley Williams' splitting pass picked out Cotterill inside the opposition half and, after taking a touch, played in Scott Sinclair who rounded Adam Federici and slotted home.
It was his ninth strike in ten this term and one that sent the travelling support into raptures, and they almost had further cause to celebrate in the preceeding minutes when both Dyer and Stephen Dobbie pulled their attempts wide.
Half-Time: Reading 0 Swans 1
David Cotterill was given the chance of extending the Swans' lead straight after the re-start after Scott Sinclair was grounded outside the area, only for his free-kick to deflect back out off the wall.
But down at the other end, meanwhile, Ashley Williams, fresh from his international adventure with Wales, twice cleared his lines to keep the Swans in the lead.
And that lead could easily have been doubled on 54 minutes when Nathan Dyer was sent clean through after working a nice one-two with Stephen Dobbie, the angle narrowed but as he pulled the trigger Federici was beaten only for the crossbar to intervene.
The Australian 'keeper made amends moments later when he denied Dobbie after he was put through by Andrea Orlandi. The Spaniard then saw a free-kick deflect inches wide of the post while Stephen Dobbie had a final touch cleared off the line when a Cotterill corner was headed goalwards by Williams.
Reading attempted to find a way back into this game and they were handed opportunites from corners as the game entered its final quarter.
And the impressive Jimmy Kebe almost stole a leveller as one such corner flew over the top of everyone and into his path, and with time he trudged towards goal and curled just over the top.
The Swans were forced to simply soak up the pressure and the home side continued to press on, and with eight minutes left on the clock Wales international Simon Church, who hadn't long replaced Shane Long, sent a close range header over goal from Kebe's cross.
Fellow replacement Noel Hunt also headed over from another corner in injury-time but the Swans held their nerve after four additional minutes to record their first win at Reading in over 25 years.