The Dynamo started well and could have taken the lead when Ricardo Clark fired an effort across the face of goal, but Cam Weaver just could not get his foot to the ball.
After the break, the visitors took the lead in spectacular fashion when Adam Moffat volleyed into the net from 25 yards out after New England failed to clear their lines from a corner.
However, New England were level were in minutes when Diego Fagundez raided down the right, shot at goal and his effort was turned into the path of Saer Sene by Tally Hall, and he made no mistake in slotting the ball home.
Houston came back into the contest and regained the lead when Moffat's shot from the edge of the area crashed off the past and hit Shuttleworth in the back and rolled into the net.
The game ended in the worst fashion for New England as they were reduced to 10 men when Dimitry Imbongo was sent off for elbowing Eric Brunner, as they fell to their sixth defeat of the season.