The Royals are still rooted deep in the relegation zone but they were the only one of the bottom three teams to get any kind of a result on Wednesday, while Southampton also drew.
It is a small step but stopping the rot was vital for Brian McDermott's men, who had come so close to earning a draw against Manchester City before Christmas.
Pavel Pogrebnyak pick-pocketed Chico Flores and Danny Guthrie carried the ball into the box before going down under the challenge of Leon Britton but the referee waved play on.
Swansea were comfortable in possession and Michu linked well with Luke Moore on the edge of the Reading box before digging out a shot which just curled wide of the top corner.
Reading defender Chris Gunter made a hash of his attempt to chest a cross from Nathan Dyer back to his keeper, and Michu pounced but somehow poked his shot over the bar from four yards out.
Although Swansea had dominated possession it was only in the final half hour they began to really test Adam Federici.
The first chance came from sloppy Reading defending, which allowed Wayne Routledge to pick out Dyer, whose diving header from eight yards out was well saved by Federici.
The Australian dealt well with a powerful drive from Ki Sung-Yeung after Reading had only half-cleared their lines from a Swansea free-kick.
Reading fans celebrated what they thought was the winner after 73 minutes when Adam Le Fondre beat Michel Vorm from close range after rising to meet Ian Harte's free-kick. But eagle-eyed referee Mike Jones spotted Le Fondre had turned the ball in with his arm and booked the Reading striker.
Source: PA
Source: PA