diff --git a/src/debugpy/adapter/servers.py b/src/debugpy/adapter/servers.py
index 0aede938..a4eb1f5c 100644
--- a/src/debugpy/adapter/servers.py
+++ b/src/debugpy/adapter/servers.py
@@ -126,11 +126,21 @@ def __init__(self, sock):
             log.info("No active debug session for parent process of {0}.", self)
         else:
             if self.pid == parent_session.pid:
-                parent_server = parent_session.server
-                if not (parent_server and parent_server.connection.process_replaced):
-                    log.error("{0} is not expecting replacement.", parent_session)
-                    self.channel.close()
-                    return
+                with _lock:
+                    # The connection can be attached to a session as soon as it
+                    # is published above, before this constructor gets a chance to
+                    # classify it. If that already happened, the connection is
+                    # established and must not be treated as an unexpected
+                    # replacement.
+                    if self.server is not None:
+                        return
+                    parent_server = parent_session.server
+                    if not (
+                        parent_server and parent_server.connection.process_replaced
+                    ):
+                        log.error("{0} is not expecting replacement.", parent_session)
+                        self.channel.close()
+                        return
             try:
                 parent_session.client.notify_of_subprocess(self)
                 return
diff --git a/tests/debugpy/adapter/test_servers.py b/tests/debugpy/adapter/test_servers.py
new file mode 100644
index 00000000..5b5a9d4b
--- /dev/null
+++ b/tests/debugpy/adapter/test_servers.py
@@ -0,0 +1,103 @@
+# Copyright (c) Microsoft Corporation. All rights reserved.
+# Licensed under the MIT License. See LICENSE in the project root
+# for license information.
+
+import threading
+
+from debugpy import adapter
+from debugpy.adapter import servers, sessions
+
+
+class FakeMessage:
+    def __init__(self, values):
+        self.values = values
+
+    def __call__(self, name, _validator, optional=False):
+        if optional and name not in self.values:
+            return ()
+        return self.values[name]
+
+
+class FakeStream:
+    name = "fake stream"
+
+
+class FakeChannel:
+    def __init__(self, stream, pid):
+        self.stream = stream
+        self.handlers = None
+        self.pid = pid
+        self.name = "fake channel"
+        self.closed = False
+
+    def start(self):
+        pass
+
+    def request(self, command, arguments=None):
+        assert command == "pydevdSystemInfo"
+        return FakeMessage({"process": FakeMessage({"pid": self.pid})})
+
+    def close(self):
+        self.closed = True
+
+
+def test_connection_waits_for_actual_session_attachment(monkeypatch):
+    # Attaching a connection stamps session.pid with the connection's pid, so a
+    # connection attached in the window after publication but before __init__
+    # classifies it by pid must survive classification rather than be closed.
+    pid = 1234
+    stream = FakeStream()
+    channel = FakeChannel(stream, pid)
+    session = sessions.Session()
+    attachment_complete = threading.Event()
+    connections = []
+    errors = []
+
+    def attach_like_a_client():
+        # Mirror the real client attach path.
+        try:
+            conn = servers.wait_for_connection(
+                session, lambda c: c.pid == pid, timeout=None
+            )
+            conn.attach_to_session(session)
+        except Exception as exc:
+            errors.append(exc)
+        finally:
+            attachment_complete.set()
+
+    def create_connection():
+        try:
+            connections.append(servers.Connection(object()))
+        except Exception as exc:
+            errors.append(exc)
+
+    def get_session(candidate_pid):
+        if candidate_pid != pid:
+            return None
+        # Block classification until the attach completes, forcing the race.
+        assert attachment_complete.wait(5)
+        return session
+
+    monkeypatch.setattr(adapter, "access_token", None)
+    monkeypatch.setattr(servers, "access_token", None)
+    monkeypatch.setattr(servers, "_connections", [])
+    monkeypatch.setattr(servers, "_connections_changed", threading.Event())
+    monkeypatch.setattr(
+        servers.messaging.JsonIOStream, "from_socket", lambda *_: stream
+    )
+    monkeypatch.setattr(servers.messaging, "JsonMessageChannel", lambda *_: channel)
+    monkeypatch.setattr(sessions, "get", get_session)
+
+    attach_thread = threading.Thread(target=attach_like_a_client, daemon=True)
+    connection_thread = threading.Thread(target=create_connection, daemon=True)
+    attach_thread.start()
+    connection_thread.start()
+    attach_thread.join(5)
+    connection_thread.join(5)
+
+    assert not attach_thread.is_alive()
+    assert not connection_thread.is_alive()
+    assert not errors
+    assert len(connections) == 1
+    assert connections[0].server is session.server
+    assert not channel.closed