Houston (2-2-4) took a 3-1 lead in the 46th minute before Sporting KC (2-2-4) scored three goals in the final 21 minutes.
Krisztian Nemeth gave Sporting KC the lead in the second minute. He gathered a Houston turnover near midfield, dribbled in space to the top of the 18-yard box and struck a ball inside the far post. Houston's Giles Barnes tied it 9 minutes later on a half-volley after Sporting's failed clearance.
Will Bruin's glancing header on Brad Davis' corner kick gave Houston a 2-1 lead just before halftime and Barnes scored from distance in the first minute after the intermission for a two-goal advantage.
Barnes sent an errant back pass toward his goalkeeper in the 74th minute that Dominic Dwyer intercepted and netted to pull Sporting KC within 3-2. Houston's Jermaine Taylor was given a red card in the 79th minute for a questionable handball in the penalty area and Feilhaber's penalty kick evened it at 3.
Raul Rodriguez put Houston back in front 3 minutes later after heading in Davis' free kick. But Feilhaber scored his second goal after a headed assist by Graham Zusi.