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 while Southampton also drew.
Victory would have flattered the hosts but there was a decent chance for Adam Le Fondre, who saw a late volley headed over the bar by Swansea defender Chico Flores while the Reading striker was also booked for handling the ball into the net.
Reading's Danny Guthrie had a penalty appeal waved away under the attention of Leon Britton in what was a rare foray forward for a side clearly focused on defence.
Swansea had plenty of 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 and missing the target a second time after turning Adrian Mariappa.
Jimmy Kebe tried to haul the game out of a growing rut with a break from his own half but a dreadful touch from Pavel Pogrebnyak on the edge of the box allowed Swansea keeper Michel Vorm to scoop up the ball.
Reading defender Chris Gunter then 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.
There was more urgency about Reading in the second half and Swansea also looked sharper as the game went on - Dyer forcing a good save from Adam Federici.
Le Fondre bundled the ball home with his arm, which was spotted by the officials, and then he volleyed goalwards only to be denied by Flores' brave defending.