I think you can simply reorder it by having the ListView (wrapped it with LinearLayout) before the DrawerLayout like this
<LinearLayout
android:layout_width="match_parent"
android:layout_height="fill_parent"
android:orientation="vertical" >
<ListView
android:id="@+id/deviceList"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:divider="#b5b5b5"
android:dividerHeight="1dp"
android:drawSelectorOnTop="false"
android:listSelector="@drawable/device_list_item_selector"
android:scrollbarStyle="outsideOverlay" />
</LinearLayout>
<android.support.v4.widget.DrawerLayout
xmlns:android="http://schemas.android.com/apk/res/android"
android:id="@+id/drawer_layout"
android:layout_width="match_parent"
android:layout_height="fill_parent" >
<ListView
android:id="@+id/left_drawer"
android:layout_width="240dp"
android:layout_height="match_parent"
android:layout_gravity="start"
android:background="#111"
android:choiceMode="singleChoice"
android:divider="@android:color/transparent"
android:dividerHeight="0dp" />
</android.support.v4.widget.DrawerLayout>
and make sure you have fill_parent for layout_height for both