Pajoy's diving header erased a 1-0 deficit and held up for a standings point that enabled United (17-10-7) to finish the regular season on a 5-0-2 run.
The result made sure D.C. would avoid the knockout round in its first playoff appearance since 2007. They will instead now have a week off to prepare to host New York in a first-round playoff series.
The news wasn't as good, however, for the Fire (17-11-7), who fell out of the Top 3 seeds in the East with the draw.
Patrick Nyarko scored on a long-distance blast in the first half for Chicago, which will now host Houston in a one-game play-in battle Wednesday at Toyota Park.
Couple mistakenly served bag of cash at McDonald's drive-thru
Kate Middleton recycles dress at movie premiere