Gylfi Sigurdsson's fifth goal in five games looked certain to give Reading yet another win until Tamas pounced with four minutes left.
Sigurdsson struck a last-minute winner at Leicester in midweek and took just six minutes to score and put Brian McDermott's side on track for their 10th win in 12 league games, but Albion were good value for their point.
This was the fourth meeting of the sides this season and the in-form home side were ahead early on.
Graham Dorrans took a corner for the visitors which Sigurdsson headed away to start a rapid counter-attack.
The ball was knocked over the top where Jobi McAnuff outpaced the Albion defence to get a shot in on goal.
Scott Carson made a fine save but the ball fell for Jimmy Kebe. He fired the rebound towards goal where a defender made a last-ditch clearance but Sigurdsson had made up the ground to tap in the loose ball for his 15th of the season.
Tamas headed wide from a Dorrans corner as the visitors looked to make a quick response before Youssouf Mulumbu was denied an equaliser by a stunning save from Adam Federici.
Both sides were throwing men forward in a fine first half hour and the Royals came close to a second.
Brian Howard did well to race onto a one-two where Carson made another brave save at his feet.
The ball looped up and Sigurdsson was again in the right place to nod it goalwards but Joe Mattock recovered superbly to head clear from under his own crossbar.
West Brom striker Chris Wood then curled wide from the edge of the box before McAnuff had the final chance of a pulsating first 45 minutes when he thrashed a shot straight at Carson at the end of a sweeping move.
Reading defender Zurab Khizanishvili tested Carson with a looping header at the beginning of the second period but the game struggled to match the tempo of the first half.
Substitute Simon Church then went close to a second for the hosts and James Morrison lashed a shot wide at the other end as the half wore on.
The equaliser came in the 86th minute and it was another Dorrans corner which did the damage.
His delivery was met by a towering header from Jonas Olsson and when the ball struck the post Tamas was on hand to smash the rebound into the roof of the net.