The Dynamo failed to find a goal in front of their home fans in the first leg of the Eastern Conference Final at BBVA Compass Stadium in Texas.
It leaves Peter Vermes' Sporting in a fine position to reach the MLS Cup decider ahead of the return leg in Kansas City on November 23.
Kofi Sarkodie appeared to have scored for the Dynamo in the first half, but his effort was ruled out for a tight offside call.
The visitors had a decent chance after a quarter of an hour when Graham Zusi teed up Jacob Peterson, who was off balance and shot wide from inside the area.
Just two minutes later, a fine team move led to Sarkodie finishing into the bottom corner, but he was ruled offside in a tight call.
Boniek Garcia's long-range free-kick tested Kansas City goalkeeper Jimmy Nielsen, who dived to his right to palm away the dangerous set-piece.
Will Bruin threatened Nielsen's goal five minutes before half-time on the counter-attack, but his fierce 35-yard drive went just over the bar.
Houston substitute Cam Weaver directed a header straight at Nielsen in the second half before Benny Feilhaber sent a shot just wide at the other end from 25 yards.
Frenchman Aurelien Collin headed a long throw-in just over the bar for Sporting and almost gave away a penalty after standing on Weaver's foot.
But after the long-range efforts and a few goalmouth scrambles, the sides had to settle for a draw heading into the second leg.
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