Etcheverry got the spot kick after Earnie Stewart was hauled down near the six-yard box by defender Alex Zotinca. It was D.C.'s first goal of the season at RFK Stadium and ended the team's 313-minute scoring drought.
Nelsen was sent off in the 54th minute after charging through Kansas City's Kerry Zavagnin. Two small scuffles flared later in the half and referee Ricardo Salazard handed out 40 fouls.
The Wizards grabbed the lead in the fifth minute as Preki dribbled uncontested up the center of the defense and fired a low, skidding shot from the top of the penalty area. The ball glanced off a D.C. defender and got by goalkeeper Nick Rimando.
Preki scored a similar goal against United in the third minute of their season opener on April 12 at Arrowhead Stadium.
Kansas City has scored first in all seven games this season and moved to 1