Houston Dynamo goalkeeper Tally Hall had made seven saves but could find no answer for CJ Sapong's stoppage-time header, and the 90th-minute equaliser extended Sporting's unbeaten run to six matches.
Brad Davis put the visiting Dynamo ahead just before the hour mark.
As Kansas City peppered Hall's goal, one of the best chances came off a free kick when Chance Myers found himself free in the box, but only managed to direct the ball straight at the shot-stopper.
Deep into stoppage time Graham Zusi collected the ball, kept his composure and lifted it to the far post, where Sapong headed home to preserve his side's unbeaten streak.
In the day's other clash, the Los Angeles Galaxy made it three consecutive wins with a 2-0 victory over the struggling Colorado Rapids.
Robbie Keane fired the hosts ahead at the Home Depot Center on 15 minutes, before Christian Wilhelmsson made sure of the result for Galaxy just prior to the hour mark.