Tony Pulis thanked Albion's 2,500 travelling fans after they inspired Albion to their first point in six games.
Albion were backed by a sell-out following after the club organised free coach travel.
It looked like it was going to be another disappointing afternoon after Sam Vokes put the hosts ahead after the breakk.
But Salomon Rondon ended his - and Albion's - goal drought with a superb finish to equalise before Craig Dawson sent the travelling Throstles into song.
Dawson's goal, on his birthday, looked to have earned Albion all three points before a defensive mix-up let Vokes nod home his second of the game with two minutes remaining.
"The lads are disappointed with the goal but overall, we’re very pleased," said Pulis.
"Our supporters were brilliant today, even when we went a goal down they were fantastic, kept behind the players and that’s good.
“Should Gareth have just headed it away and not let Ben get involved? I’m not sure but we are what we are.
“Gareth and Ben have been brilliant for us all season."
Have your say on Albion's point here at Baggies Banter.