Rooney was not permitted to officially take charge of D.C.(6-12-3, 21 points), where he previously played in 2018 and 2019, until his visa paperwork was finalized earlier this week.
Fountas' goal, on a first-time volley of Kimarni Smith's cross in the fifth minute of stoppage time, was his team-leading 11th of the season.
Durkin's, on another one-time finish from Ola Kamara's service only three minutes earlier, was his first since returning from St. Truiden in the Belgian first division.
Junior Urso scored his third goal of the season in the ninth minute for Orlando (8-9-6, 30 points), which lost for just the third time on the road this season.
Pedro Gallese made two stops for Orlando, which has now lost two straight and is winless in its last four but remains fifth in the Eastern Conference.
Alexandre Pato contributed his fifth assist of the year for the visitors, who were swept in the season series after falling 5-3 at home earlier this month.
Pedro Gallese best stop came in the 61st minute on Fountas, who hammered a one-time volley from close range into his trailing leg.
That was as close as D.C. came until the late drama.
First Smith found Kamara wide to the left of the penalty area, and Kamara drove a low cross toward the penalty spot where Durkin hammered a finish in stride into the top left corner.
Not long after play restarted, Martin Rodriguez began the next goal-scoring attack with a probing long ball to the same left corner. This time Smith hit the cross on the volley, and Fountas guided a gentle finish into the bottom right corner to send the home fans into delirium.