Playing through a steady rain at RFK Stadium, United (0-2-1) extended its club-record winless streak in league play to 15 games dating to the 2013 season. It's the fifth-longest streak in MLS history.
Jhon Kennedy Hurtado scored in the 27th minute for Chicago (0-1-3), which has ties in each of its last three matches after a season-opening loss.
United lost all three games against Chicago last season and have not beaten the Fire at home since 2012.
The Fire grabbed a first-half lead off a Harrison Shipp corner kick for the second consecutive game. Hurtado found space in between two United defenders and headed home the cross for his first goal of the season and just his second since joining MLS in 2009.
After failing to score in their opening two games of the season, United drew even when Espindola converted a left-footed shot in the 35th minute. D.C. earned the free kick after Eddie Johnson was tackled just outside the box. Nick DeLeon then stepped over the ball before heeling the free kick back to Espindola, who scored his first goal since coming over from the New York Red Bulls in the offseason.
United took the lead in the 73rd minute when Kitchen cleaned up a scrum in front of the Chicago goal, slotting home United's fourth chance after the ball bounced off Fire defenders and the goalpost.
Chicago goalie Sean Johnson had six saves, including four in the first half.