The home side end a seven-game losing streak and reach double figures on points but remain in the relegation zone, while the visitors have now gone four matches without a victory
The Swans had most of the better chances, Michu somehow missing from six yards in the first half and Nathan Dyer being denied by an excellent Adam Federici save after the break.
But the home side improved as the game wore on and almost nicked a priceless victory when only a headed goal-line clearance from Chico denied Adam Le Fondre.
It was not the result for which either side would have hoped, although the hosts move off the bottom of the Premier League table and finally hit double figures on points. Swansea remain in mid-table but have now gone four games without a win.
Reading had no fresh injury concerns for the game, with Jason Roberts, Sean Morrison and Alex McCarthy all still out. Ki Sung-Yueng returned to Swansea's starting XI, although an anticipated return for winger Pablo Hernandez from his thigh injury did not materialise.
The Swans made a bright start to proceedings but there were no early openings until both side had golden opportunities at either end of the pitch. Pavel Pogrebnyak was played through on goal but miscontrolled at the vital moment to squander the chance.
Then, at the other end, the usually reliable Michu somehow failed to open the scoring with an even better opening. Chris Gunter failed to play the ball back to Federici but, as the ball fell at the feet of the Spaniard with the goal gaping from six yards, he somehow fired his shot over the crossbar.
Swansea continued to have comfortably the better of the first half, dominating possession without creating too many clear-cut chances. Dyer missed the target with two long-range efforts before the half-time whistle was blown with the score still goalless.
The home side started the second half slightly better and Jobi McAnuff missed the target on 54 minutes after the ball deflected into his path when Pogrebnyak took a tumble in the box.
Swansea were unhappy when the big striker escaped with only a booking for making two fouls in a matter of seconds. Reading responded with a double change, taking the Russian off along with McAnuff as Hal Robson-Kanu and Le Fondre came on after an hour.
The visitors were still looking most threatening, though, and only a stunning reaction save from Federici denied Dyer from a close-range header after good work from Wayne Routledge out wide after 65 minutes.
The Royals keeper had to get down smartly again to deny Ki before Reading had the ball in the net. The lively Le Fondre rose to divert a free kick past Michel Vorm but the goal was rightly disallowed and the striker booked for using his hand.
There was a concerning sight for away fans in the latter stages as Michu hobbled off the pitch with what looked like an ankle injury.
Reading almost snatched a late winner but Chico brilliantly prevented a goal from a sweetly struck Le Fondre effort.