The goal was Pereyra's first of the season and third in 25 career matches for Orlando City.
Goalkeeper Pedro Gallese notched his third shutout of the campaign for Orlando City, which is unbeaten despite scoring just six goals this season. The Lions have allowed just two.
D.C. United lost for the fourth time in their past five matches.
D.C. United held a 13-6 edge in shots but placed just one on target. The Lions also had just one on goal.
Pereyra struck in the seventh minute on a goal set up by Tesho Akindele.
Pereyra was operating in the box and sent a right-footed shot past D.C. United goalkeeper Jon Kempin.
D.C. United was unable to create opportunities in the latter stages. Ola Kamara tried to create one of his own during the second minute of stoppage time but his bicycle kick was well off the mark.
Being behind most of the match had D.C. United pushing the pace and they had 10 corner kicks to Orlando City's two.
D.C. United had three solid chances in the first 27 minutes of the second half.
Paul Arriola was in good position in the 48th minute but sent his right-footed shot wide to the left.
Gressel took another free kick 11 minutes later and sent a cross in toward Kamara, who somehow wasn't able to get a foot on it and Gallese collected the ball.
Both teams had their only on-target shot in the first half. D.C. United took six in the half, while Orlando City had four.