Darren Pratley's second-half strike sent the Swans up into the Championship's top-two.
He slotted home the winner on 65 minutes as Angel Rangel knocked-down Mark Gower's free-kick into the penalty area.
It marked the first 'double' of the campaign and the Swans went into the game at Leicester two days later in their highest league position for over 27 years.
Garry Monk was back in the side after missing the win against Barnsley four days earlier.
The club captain had also re-taken the armband as Alan Tate, who played against the Tykes, was missing through suspension.
There were three other changes to the starting line-up with Darren Pratley, Joe Allen and Scott Sinclair replacing Mark Gower, David Cotterill and Jermaine Easter, all of whom dropped to the bench.
Swans:Dorus de Vries; Angel Rangel, Garry Monk(C), Ashley Williams, Neil Taylor (Albert Serran, 28'); Joe Allen, Andrea Orlandi (Mark Gower, 23'), Darren Pratley; Nathan Dyer, Scott Sinclair, Stephen Dobbie (Jermaine Easter, 71').
Not Used:Yves Makabu-Makalambay (GK), Kemy Agustien, David Cotterill, Craig Beattie.
Reading: Adam Federici; Andy Griffin, Matt Mills (C), Alex Pearce, Ian Harte; Brian Howard, Jay Tabb (Noel Hunt, 80'), Jimmy Kebe, Hal Robson-Kanu (Michail Antonio, 72'); Simon Church, Shane Long
Subs: Alex McCarthy (GK), Shaun Cummings, Zurab Khizanishvili, Jem Karacan, Jake Taylor.
Attendance: 14,329 Away: 580
Referee: S A Hooper (Wiltshire)
The home side made an explosive start to life in 2011 and it could have been even better had their early attempts beaten Reading 'keeper Adam Federici.
Spirits were high following the win against Barnsley four days earlier and within two minutes of this game starting Andrea Orlandi earned his side a corner after a dazzling run down the left.
And it was from his corner that picked out the unmarked Ashley Williams inside the box but his strike was blocked by his own team mate, Garry Monk.
Darren Pratley also saw an attempt blocked while Orlandi came close from 20-yards. The pair combined forces 11 minutes to force Federici into saving on his line as Orlandi powered a diving header at goal from Pratley's by-line cut-back.
But despite the champagne football on show from the slick Swans there came a short spell where Reading threatened - Alex Pearce's drive was deflected for a corner and from Brian Howard's delivery the ball made its way back to the same player and his shot was smothered and pushed wide by Dorus de Vries.
The Swans suffered a blow midway through the half, though, as Orlandi was forced off to be replaced by Mark Gower; and within minutes it looked as if Neil Taylor would follow suit after coming off worse in a tackle, but after some treatment he was able to continue.
He only lasted a matter of minutes, however, before deciding that he had no choice to go off and Albert Serran was sent off to play in his first game since late November.
Reading settled and attempted to use the counter attack to their advantage and with a little more than 10 minutes before the break Wales international Simon Church was given acres of space but sliced his strike wide.
Stephen Dobbie was denied by Federici moments later but the visitors could have snuck in at the break ahead but Church couldn't properly connect with Kebe's cross in the closing stages.
Half-Time: Swans 0 Reading 0
The second period also saw the home side start brightly and they threatened from Mark Gower's corner early on, Scott Sinclair got half a touch inside the area and as it whistled across the box Ashley Williams made contact only to be penalised by the referee for a foul.
Dorus de Vries' legs came to the rescue 10 minutes in as he denied Church with one of the game's better chances, while Angel Rangel found space outside the area but sent his shot across goal and wide.
But just after the hour the Swans made their efforts count to take this game by the scruff of the neck.
Brian Howard was pulled up for a fould on Darren Pratley just outside the area, Mark Gower's delivery was fired back across goal by Rangel and Pratley was placed to side foot beyond Federici and into the net.
The Liberty Stadium errupted as the midfielder found the net for the fifth time this season, but Reading were keen to get themselves back into this contest pretty sharping.
Garry Monk twice blocked the advances of Jimmy Kebe and Church inside the area, Ian Harte found the stand with a free-kick while skipper Matt Mills sent a header over from a corner.
But there was no argument that the Swans were on top as the game entered the closing stages and Scott Sinclair twice came close to extending the lead, though Simon Church wasted a great chance six minutes from time when he sent a free header over the bar from six-yards.
The home side had an even great chance two minutes later, however, as Scott Sinclair burst forward from inside his own area and into the Reading box - he could have gone it alone but opted to play in Nathan Dyer, he only had the 'keeper to beat but after taking a little too much time he was denied a shot at goal.
Reading threw everything at the Swans in the dying minutes as keeper Adam Federici went forward for a corner. But de Vries punched clear and as Sinclair raced in on goal from the halfway line, the winger delayed his shot with Federici way out of his goal and his effort was blocked.
It didn't matter though as the Swans climbed into second place.