The Royals wing-back's unstoppable strike earned a hard-fought point and ended their three-game losing streak in the league.
It looked as if Swansea were set to reclaim top spot after protecting the lead given to them by Borja Baston's early header after just three minutes.
The Spanish striker's sixth goal of the season sent him to the top of the goalscoring charts but could not stop Swansea's winless run extending to four matches in all competitions.
The visitors avoided a fourth-straight defeat ahead of another two testing matches against Fulham and Bristol City.
Reading showed signs of revival despite exiting the Carabao Cup after a penalty shoot-out defeat against Wolves in midweek.
The Swans' flying start to the season had hit a speed bump after a draw and a defeat in their previous matches, but they raced into the lead after three minutes.
Borja spotted his opportunity, moved into the space and glanced in a header for his sixth league goal of the season.
But Ayew looked determined to double Swansea's lead. First he surged down the right and hit the side netting, before he was put one-on-one with Rafael Cabral following a rapid breakaway by Bersant Celina and Borja.
The Royals goalkeeper rushed out and got to the feet of the Swansea forward to smother his effort.
Lucas Boye was lucky to avoid a second yellow on the stroke of half-time for tugging back Matt Grimes after his earlier booking for a late challenge on Connor Roberts.
But the breakthrough finally came when Yiadom was given space and time on the edge of the box to fire a lethal shot across the face of goal and past Freddie Woodman into the top corner to snatch a share of the points.