Chicago (2-0-2, 8 points) won its second straight.
Kansas City (1-3-0, 3 points) has lost two in a row and scored only three goals through four games to start the season.
The home side held the possession advantage in the first half, with nearly 60 percent of the touches. But it didn't amount to much offensively, with just two shots attempted, one on goal.
Both sides struggled to generate any form of attack, making pass after pass outside the box or near midfield but not getting anywhere close to the area for a quality opportunity.
Przybylko broke the ice to give the Fire a 1-0 lead in the 30th minute.
Xherdan Shaqiri forced a turnover at midfield at dished off to Fabian Herbers. Herbers sent it to his left to Przybylko, whose shot from inside the box went through goalkeeper Tim Melia's hands and legs into the back of the net.
It was his first goal with the Fire and the side's first tally on its home field this season.
Shaqiri converted on a penalty kick to put Chicago ahead 2-0 in the 50th minute, fooling Melia into thinking he'd shoot left before scoring into the bottom right corner.
Roger Espinoza quickly responded for Sporting, finishing off quick passing at the top of the goal area to cut it to 2-1 in the 56th minute. It was the first goal the Fire have conceded this season, ending their shutout streak at 326 minutes.
Przybylko made it 3-1 in the 82nd minute. Brian Gutierrez showed patience as he came down the right side before sending a cross to the German striker outside the goal area.