Giles Barnes proved a constant threat to the Philadelphia defence and had a number of chances to score before the interval, but failed to make the important breakthrough.
Less than a minute after the restart, Union came close to breaching the Dynamo defence when Casey unleashed a shot that was saved by keeper Tyler Deric down to his right.
Barnes then wasted an excellent chance to give Houston the lead when he met a Brad Davis corner, but his close-range effort was high and wide.
Houston nearly punished the Philadelphia's wayward shooting when Omar Cummings flashed a late effort inches wide of the Union goal.
In the end, both side had to settle for a point and the result leaves Union behind fifth-placed New York Red Bulls in the Eastern Conference and outside of the playoff positions with time running out in the regular season.