A superb long-range strike from Adam Moffat in the 18th minute and then a cool finish from Will Bruin 15 minutes from the end gives Dynamo a two-goal lead to take into Wednesday's second leg in Kansas City.
Scottish midfielder Moffat latched on to a loose ball and fired a magnificent right-foot shot from 30 yards beyond the reach of KC keeper Jimmy Nielsen to put Dynamo, two-times MLS Cup winners, in front.
Bruin wasted a great chance in the 38th minute when he was found inside the area by Honduran midfielder Oscar Boniek Garcia, but miskicked from a promising position.
Sporting struggled to create openings but let an opportunity go begging in the 70th minute when US international Graham Zusi shot wide from inside the area.
Dynamo made KC, who had the best regular season record in the East, pay for missing that chance with a second goal in the 75th - Calen Carr raced down the left flank and picked out Bruin who calmly converted with the side of his foot.
The winner will meet the victor from the other Eastern Conference semi-final between New York Red Bulls and DC United, which stands at 1-1 after the first leg.
In the Western Conference semi-finals first legs, the LA Galaxy were due to face the San Jose Earthquakes later on Sunday while Real Salt Lake drew 0-0 on Friday at the Seattle Sounders.
Houston Dynamo v Sporting Kansas City match data
Will Bruin was on the pitch for 84 minutes against Sporting Kansas City. The striker scored in the 75th minute and assisted on Moffat's goal in the 18th minute.
Houston Dynamo finished with a clean sheet thanks to the strong play of the team's defense and Tally Hall, who finished with one save. Houston Dynamo had 19 tackles, four blocked shots and 55 total clearances in support. Brian Ching made a big difference on the match after coming on for Calen Carr in the 81st minute, as he took two shots. Ricardo Clark had three shots for Houston Dynamo, more than any of his team-mates.
Sporting Kansas City had 51.3% of the possession during the loss. They had 13 shots, including one on target. The four attempts by Graham Zusi were the most of any Sporting Kansas City player.
While Sporting Kansas City ended up winning the possession battle over the duration of the match, Houston Dynamo reached half time having controlled the ball for 54.8% of the contest's first stanza. Houston Dynamo led at half-time even though they only attempted four shots compared to Sporting Kansas City's five.
Houston Dynamo are five points behind D.C. United and a spot in the UEFA Champions League, while in fifth place with a record of 14 wins, nine losses and 11 draws. Sporting Kansas City sit atop the table with 63 points and an overall record of 18 wins, seven losses and nine draws.