D.C.'s 2012 murder rate actually put it at only 19th among U.S. cities, below such "homicide capitals" as Buffalo, Milwaukee, and Oklahoma City.
There are many factors that have contributed to D.C.'s crime turnaround, but removing guns from criminals certainly is among them. I don't pretend to know how much of a role this played versus, say, removing lead from our drinking water and air, but I suspect it is a significant factor.
Homicide rate started falling after implementing and anti-gang task force in DC. Gangs don't get concealed handgun licenses. Also, the wiki you reference includes manslaughter. DC is a perpetual top-10 for homicide stats.
Unfortunately, the homicide rate rose sharply in 2013, due to the Navy shipyard shooting. Homicide rate was up sharply through the first half of 2014, as well. Violent crime is down, but homicide continues to plague the capital.