Having won the opener of the two-match, aggregate-score semifinal series 2-0, Houston will now meet either New York or D.C. United for a berth in the MLS title game.
Wednesday's second-leg matchup between New York and D.C. United was postponed in Harrison, N.J., due to snow. It will be played on Thursday with the teams having battled to a 1-1 tie in their first meeting.
Kansas City produced an almost continuous bombardment on the Houston goal as the Dynamo, starting the game with a two-goal lead, chose to put up a tight defensive effort.
Houston's strategy paid off, although Kansas City got one of the two goals it needed in the 64th minute when Seth Sinovic put a header past Hall for his first score of the season.
The Dynamo advanced through two post-season rounds after earning the fifth and final playoff berth in the Eastern Conference. Houston downed Chicago in the first-round knockout game 2-1 before surviving the two-match series against Kansas City -- which owned the best regular-season record in the conference.
Houston will host the first leg of the conference finals next Sunday.