Dynamo were the first to threaten as they put a decent passing move together to set up Corey Ashe, who sent his shot just over the bar in the seventh minute.
The hosts were ahead less than 10 minutes later as Brad Davis curled a cross into the middle for Will Bruin to nod home for the opening goal.
Davis almost got his own name on the scoresheet midway through the half as he tested Donovan Ricketts from outside the box. The Portland keeper spilled the effort but was let off the hook as Boniek Garcia could only find the side-netting with the rebound.
The visitors got their equaliser shortly after the half-hour mark as Khalif Alhassan's pass deflected into the path of Gaston Fernandez, who made no mistake with his finish.
Neither side could find a winner in a second half short of goalmouth action as the spoils were shared in Houston.