The visitors thoroughly deserved to be ahead but Gylfi Sigurdsson drew Reading level with a superb free-kick in first-half stoppage time.
Reading pushed for the lead at the start of the second half but the best chance fell to Swansea with Gorka Pintado's header forcing Adam Federici into a fine save.
The result left Swansea four points behind the automatic promotion spots, while Reading moved up to 19th.
Swansea made a bright start and had a glorious chance to make it 1-0 with just 13 minutes gone when Brynjar Gunnarsson's clearance was deflected into the patch of Nathan Dyer, but Reading goalkeeper Federici made a smart stop with his legs.
Pintado was off target with another chance for the visitors moments later before Reading eventually began to find their rhythm.
Shane Long nodded the ball into the path of Grzegorz Rasiak, who chested the ball up before volleying over from 25 yards.
However, Swansea continued to look the brighter of the two sides and Andrea Orlandi had a shot from the edge of the box but Federici was on hand to make the save.
Orlandi was involved again soon after with a free-kick that looked to be heading into the path of Pintado but Federici was alert to gather the ball on the bounce.
The goal appeared to be coming and so it proved with 35 minutes gone when some neat interplay resulted in a fine through-ball from Orlandi for Pratley, who finished superbly past Federici.
It was no more than Swansea deserved but, in first-half stoppage time, Dyer fouled Sigurdsson 25 yards from goal and he picked himself up to curl an excellent equaliser into the bottom-left corner.
Buoyed by their equaliser, Reading came flying out of the traps at the start of the second period. Jobi McAnuff lofted the ball into Rasiak, who controlled before firing wide.
Sigurdsson then sent a long-range effort over the bar before Long was forced off injured and replaced by Jimmy Kebe.
The Malian made an immediate impact with a mazy run, beating several challenges and winning a corner off Alan Tate.
However, Swansea always looked dangerous and could have been back in front just after the hour mark when Orlandi crossed for Pintado who headed goalwards but Federici got down well to make a good save.
Lee Trundle had the ball in the back of the net for Swansea late on but the goal was ruled out for offside as Reading hung on.