Birchall, in his sixth game after being signed in May following three seasons with Los Angeles, ran past the D.C. line to take a leading ball from Jairo Arrieta. Birchall dribbled down the left side and scored from 10 yards out with his left foot for his first goal with the Crew (7-7-4).
''As (Arrieta) he turned inside I noticed no one was going to trap me,'' Birchall said. ''He spotted me out of the corner of his eye and played a great ball. From there it was trying to take a good first touch and seeing the keeper come out, I tried to drill it under him, really.''
Columbus goalkeeper Andy Gruenebaum made three saves for his seventh shutout.
United (10-7-3) missed a chance to tie the match in the 88th minute when Chris Korb struck the left post with his 18-yarder.