Angel's goals came in the 19th and 21st minutes, while a big penalty-kick save by net-minder Jon Conway in the 53rd minute clinched third place in the Eastern Conference for the Red Bulls (12-11-6), as they stopped a four-game winless streak.
The Wizards' goal was scored by Jack Jewsbury in the 21st minute.
With its loss, Kansas City (10-12-7) squandered a chance to qualify for a playoff berth.
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