He fired home from close range after Jonas Olsson's effort had rebounded from the bar.
An early goal by Gylfi Sigurdsson had put Reading ahead in the battle between the top two form sides in the Championship.
A thrilling game saw both sides playing open and attacking football with the better chances falling to Reading, who went ahead in the seventh minute following a dash down the left flank by Jobi McAnuff.
He raced forward only to see his shot saved by West Brom keeper Scott Carson.
The ball rebounded to Shane Long, whose shot was also blocked. This time the ball ran free to the unmarked Sigurdsson, who calmly side-footed it into an empty net.
West Brom tried to hit back straight away and from a corner Tamas saw his effort superbly tipped over the bar by Adam Federici.
Federici then made a fine one-handed save from James Morrison and an easier one from dangerman Graham Dorrans
There was a fortunate escape for West Brom midway through the first half when Joe Mattock found himself standing in the perfect place to head Sigurdsson's header off the line.
Reading came close to a second early in the second half when Sigurdsson found Long in space. He sent the ball forward to Jimmy Kebe but Carson just managed to race out in time to block the winger's shot.
Reading survived loud West Brom appeals for a penalty for handball by Matt Mills which referee Andy D'Urso ignored.
With just under half an hour to go, West Brom put on Ishmael Miller and Giles Barnes, taking off Youssouf Mulumbu and Chris Wood.
Shorty afterwards Simon Church replaced Shane Long for Reading and with almost his first touch he got on the end of a ball from Sigurdsson and put his shot just wide of the post.