There are post emergent herbicides labeled for stiltgrass, however, we do not have research on their effectiveness.
In general your best option for control in lawns is using a preemergent herbicide a couple of weeks before crabgrass seeds germinate the spring. Seedlings emerge about the same time as crabgrass. Barricade and Pendulum are the most effective ones for this particular weed out of the many preemergents to choose from.
Keep the area mowed to help prevent the stiltgrass from forming seeds. Overseed in the fall to thicken your stand of turf.
See our website for more information http://extension.umd.edu/hgic/japanese-stiltgrass