Philadelphia, on the other hand, had been shut out in three of its previous four games and had not scored a goal during run of play for 360 minutes plus stoppage time.
The Union also was winless in nine games, with several potential victories given away with late goals.
So when Sporting KC's Dom Dwyer scored in the 80th minute, everything seemed headed toward a 10th straight winless effort for Philadelphia.
That's why soccer is such a strange sport. Just when you think you've got something figured out, everything changes.
Just a minute after Dwyer scored, Cristian Maidana put home his first goal as a member of the Union, which stood up as the winner in an improbable, season-saving, 2-1 victory.
Maidana, the midfielder from Argentina who was signed this season, had also set up Philadelphia's first goal - by Danny Cruz, who had not scored since Aug. 25, a span of 19 matches.
"Credit to our guys who really fought through tonight," said Union coach John Hackworth, who for a change did not have to repeat his "We played well enough to win but just did not" speech. "It wasn't our best soccer, but we grinded it out and picked up three huge points against one of the best teams in MLS.
"We got the goals when they mattered, and the response after the Kansas City goal was fantastic."
If this wasn't exactly a "must"win, it was about as desperate a situation in which a team could find itself a third of the way through a season.
While Hackworth and the Union players kept expressing their belief that they were going to pull things together and start winning matches, the stress of the winless streak was wearing them down.
"Individually, this is when your character needs to come out with extra effort and your level needs to be there," Philadelphia captain Brian Carroll had said after last Saturday's 1-0 loss at home to rival D.C. United. "Whatever event needs to occur for us to get a win and get back on the right track, we need to find it."
It's just the first step out of the hole the Union has dug for itself, but it certainly beat falling in deeper.
While team CEO Nick Sakiewicz had given Hackworth a strong vote of confidence a couple of weeks ago, everyone at PPL Park on Saturday heard the chants of "Fire Hackworth" coming from the crowd late in the loss to D.C.
"I certainly heard the fans on Saturday and it's impossible not to hear a lot of the talk," Hackworth had said leading into the match at Sporting KC. "I tried to be very diligent of staying away from reading stuff in the press lately.
"The reality is that it is impossible not to be affected by it, and I wouldn't say as much me as the players."
The players have all expressed continuing support for their embattled manager, but action finally spoke louder than words.
"We're behind [Hackworth] and he knows we are behind him," Cruz said. "We just wanted to show the media and the fans that tonight was big for not just us but for [Hackworth], and I think you could see the fight in everybody tonight for that big reason."
The Union players needed to prove something to themselves more than to the media and fans. Still, whatever the motivation, the key now is for the Union (2-5-5) to keep it flowing with more positive results.
The much-needed three points from the win over Sporting KC raises Philadelphia's total to 11 - moving it within six points of first in the Eastern Conference.
Co-leader New England comes to PPL Park tomorrow, and getting another three points would be a boost for the Union.
Philadelphia's other win came in its home opener against New England.
It's really another "must" win because the Union's 12 matches are the most that have been played in MLS.
The Revolution and Sporting KC have two games in hand over the Union and third-place D.C. United (14 points) has only played nine matches.
Philadelphia has four more matches before MLS goes on its 3-week World Cup break after the June 7 game against Vancouver.
Having already given away at least a half-dozen points because of late-game collapses, the Union no longer can settle for ties.
"Everyone feels pretty confident in the offense, especially after scoring two goals," Union goalkeeper Zach MacMath said. "Two scores in the run of play is really good for our confidence.
"Now it's about taking that into this match against New England and finishing out this streak on a high note."