The Dynamo (6-5-7) had their best late opportunity in the 90th minute on a shot by Brian Ownby, but Nielsen and defender Aurelien Collin combined to make the stop.
Sporting (10-5-3) had an excellent chance on Kei Kamara's header in the 47th, but it went right to Hall, who made a clean save on the attempt.
Houston extended its unbeaten string to three matches while Kansas City used the single standings point to move back into a share of the Eastern Conference lead with D.C. United at 33 points.
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