Trailing 2-1 at the end of regulation time, Jalil Anibaba equalised for the home side in the 91st minute before former Liverpool striker Krisztian Nemeth completed the dramatic comeback three minutes later at Sporting Park.
The win sent Sporting KC into fourth in the West, level on eight points with Real Salt Lake, who edged San Jose Earthquakes 1-0.
The Union - bottom of the Eastern Conference - thought they had the match sewn up thanks to Fernando Aristeguieta's strike and Jacob Peterson's own goal, split by Dominic Dwyer's 16th-minute equaliser for Sporting.
Peterson handed the visitors a third-minute lead after putting the ball past goalkeeper Luis Marin, though Dwyer restored parity 13 minutes later courtesy of a powerful header from a corner.
But Aristeguieta restored the Union's lead within three minutes when he headed beyond Marin for his third goal of the season.
With the Union seemingly destined for their first win of the campaign, Anibaba and Nemeth, who scored the club's 1000th competitive goal, sent the home faithful into raptures during stoppage time following last week's 1-0 win at New York City.
Javier Morales silenced a capacity crowd at Avaya stadium as Real Salt Lake edged the Earthquakes 1-0.
Morales gave RSL a 44th-minute lead in sensational fashion after firing a long-range shot off the underside of the crossbar, having cannoned his free-kick into the wall.
That goal proved the difference as RSL built on last week's 2-1 win over Toronto FC.
