The Reds looked like the superior side throughout the contest, with Ayo Akinola scoring twice to give them a two-goal lead at halftime.
The Canadian club's chances of winning the match were also boosted after D.C. United midfielder Junior Moreno picked up a second yellow card for a reckless tackle on Marky Delgado just before the break.
But D.C. United managed to prevent TFC from adding to their lead before getting back into the match and overturning a two-goal deficit with less than 10 minutes remaining.
Federico Higuain scored in the 84th minute with a lovely chip over TFC goalkeeper Quentin Westberg before Frederic Brillant completed the comeback with an injury-time equalizer.
The two teams were initially scheduled to play Sunday morning, but the game was called off moments before kickoff after D.C. United reported a positive coronavirus test and one Toronto player received an inconclusive result.
Further testing revealed that all players on both teams tested negative, but the two players that prompted Sunday's postponement were held out of Monday's draw and will undergo another round of testing.
Toronto FC will take on the Montreal Impact on Thursday, while D.C. United will face the New England Revolution on Friday.