Dynamo pressed forward through Brad Davis who unleashed a powerful strike towards the bottom corner, but Melia got down low to his right to parry the ball behind.
Dwyer continued to cause problems for Sporting as he timed his run to the near post to latch on to Feilhaber's cross, but he put his header inches wide of the post.
The home side had an excellent chance to double their lead when Krisztian Nemeth raided forward into the box and cut the ball back for Dwyer, but with the goal at his mercy, his effort was blocked by David Horst.
Houston capitalised on the play by Horst as they equalised two minutes later when Ricardo Clark headed Davis's free kick beyond Melia into the net.
The visitors ended the game with 10 men after Nathan Sturgis was dismissed for a poor challenge on Roger Espinoza, while Nemeth looked to have stolen the win for the home side at the death with a powerful strike, but his effort was ruled out for offside.