diff --git a/folium/plugins/draw.py b/folium/plugins/draw.py
index 7d54f1805d..2de7733bbd 100644
--- a/folium/plugins/draw.py
+++ b/folium/plugins/draw.py
@@ -58,9 +58,8 @@ class Draw(JSCSSMixin, MacroElement):
         {% macro html(this, kwargs) %}
             {% if this.export %}
             <style>
-                #export {
+                #export_{{ this.get_name() }} {
                     position: absolute;
-                    top: 5px;
                     right: 10px;
                     z-index: 999;
                     background: white;
@@ -74,7 +73,7 @@ class Draw(JSCSSMixin, MacroElement):
                     top: 90px;
                 }
             </style>
-            <a href='#' id='export'>Export</a>
+            <a href='#' id='export_{{ this.get_name() }}'>Export</a>
             {% endif %}
         {% endmacro %}
 
@@ -123,14 +122,14 @@ class Draw(JSCSSMixin, MacroElement):
             });
 
             {% if this.export %}
-            document.getElementById('export').onclick = function(e) {
+            document.getElementById('export_{{ this.get_name() }}').onclick = function(e) {
                 var data = drawnItems_{{ this.get_name() }}.toGeoJSON();
                 var convertedData = 'text/json;charset=utf-8,'
                     + encodeURIComponent(JSON.stringify(data));
-                document.getElementById('export').setAttribute(
+                document.getElementById('export_{{ this.get_name() }}').setAttribute(
                     'href', 'data:' + convertedData
                 );
-                document.getElementById('export').setAttribute(
+                document.getElementById('export_{{ this.get_name() }}').setAttribute(
                     'download', {{ this.filename|tojson }}
                 );
             }
diff --git a/tests/plugins/test_draw.py b/tests/plugins/test_draw.py
new file mode 100644
index 0000000000..16889b1aea
--- /dev/null
+++ b/tests/plugins/test_draw.py
@@ -0,0 +1,70 @@
+"""
+Test Draw
+---------
+"""
+
+import re
+
+import folium
+from folium import plugins
+from folium.template import Template
+from folium.utilities import normalize
+
+
+def test_draw():
+    m = folium.Map([45.0, 3.0], zoom_start=4)
+    draw = plugins.Draw(export=True, filename="my_data.geojson")
+    m.add_child(draw)
+
+    out = normalize(m._parent.render())
+
+    # Verify that the export button has been created with a unique id.
+    tmpl = Template("<a href='#' id='export_{{this.get_name()}}'>Export</a>")
+    assert normalize(tmpl.render(this=draw)) in out
+
+    # Verify that the style targets that same id.
+    assert normalize(f"#export_{draw.get_name()} {{") in out
+
+    # Verify that the click handler is wired to that same id.
+    assert (
+        normalize(f"document.getElementById('export_{draw.get_name()}').onclick") in out
+    )
+
+
+def test_draw_no_export():
+    m = folium.Map([45.0, 3.0], zoom_start=4)
+    draw = plugins.Draw()
+    m.add_child(draw)
+
+    out = normalize(m._parent.render())
+
+    assert "Export</a>" not in out
+    assert f"export_{draw.get_name()}" not in out
+
+
+def test_two_draw_controls_get_unique_export_ids():
+    """Each Draw gets its own export button, wired to its own layers.
+
+    A hard-coded ``id='export'`` made the second button dead and pointed the
+    first at the wrong FeatureGroup.
+    """
+    m = folium.Map([45.0, 3.0], zoom_start=4)
+    first = plugins.Draw(export=True, filename="first.geojson")
+    second = plugins.Draw(export=True, filename="second.geojson")
+    m.add_child(first)
+    m.add_child(second)
+
+    out = m._parent.render()
+
+    ids = re.findall(r"id='(export_[^']+)'", out)
+    assert len(ids) == 2
+    assert len(set(ids)) == 2, f"export button ids are not unique: {ids}"
+
+    # Each handler must reference its own element, layers and filename.
+    for draw, filename in ((first, "first.geojson"), (second, "second.geojson")):
+        element_id = f"export_{draw.get_name()}"
+        assert f"id='{element_id}'" in out
+        start = out.index(f"document.getElementById('{element_id}').onclick")
+        handler = out[start : out.index("}", start) + 1]
+        assert f"drawnItems_{draw.get_name()}.toGeoJSON()" in handler
+        assert filename in handler