diff --git a/src/mcp/server/streamable_http.py b/src/mcp/server/streamable_http.py
index b6128d3e0..7e2c8923d 100644
--- a/src/mcp/server/streamable_http.py
+++ b/src/mcp/server/streamable_http.py
@@ -646,7 +646,14 @@ async def _handle_post_request(self, scope: Scope, request: Request, receive: Re
                 INTERNAL_ERROR,
             )
             await response(scope, receive, send)
-            await writer.send(Exception(err))
+            # The session's read stream may already be closed (e.g. the session task
+            # crashed and tore down its streams before this handler ran). Sending into a
+            # closed/broken stream here would raise a secondary error that masks the
+            # original one and surfaces as "Exception in ASGI application". Guard it.
+            try:
+                await writer.send(Exception(err))
+            except (anyio.ClosedResourceError, anyio.BrokenResourceError):  # pragma: lax no cover
+                pass
             return
 
     async def _handle_get_request(self, request: Request, send: Send) -> None:
diff --git a/tests/server/test_streamable_http_router.py b/tests/server/test_streamable_http_router.py
index 3086dca99..4b8501daa 100644
--- a/tests/server/test_streamable_http_router.py
+++ b/tests/server/test_streamable_http_router.py
@@ -114,3 +114,59 @@ async def asgi_send(message: Message) -> None:
     assert sent[0]["status"] == 500
     body = b"".join(m.get("body", b"") for m in sent if m["type"] == "http.response.body")
     assert b"backend unavailable" not in body
+
+
+@pytest.mark.anyio
+async def test_post_error_path_tolerates_closed_session_stream() -> None:
+    """The error path must not raise a secondary error when the read stream is gone (#2741).
+
+    When a session task crashes it tears down its read stream before the concurrent
+    POST handler reaches its `except` block. The trailing ``writer.send(Exception(err))``
+    then targets a closed/broken stream. Without a guard that raises a secondary
+    ``ClosedResourceError``/``BrokenResourceError`` out of the ASGI app, masking the
+    original error and surfacing as "Exception in ASGI application". The 500 response
+    must already be delivered and ``handle_request`` must return cleanly.
+    """
+    transport = StreamableHTTPServerTransport(
+        mcp_session_id=None,
+        is_json_response_enabled=False,
+        event_store=_PrimingFailingStore(),
+    )
+
+    body = b'{"jsonrpc":"2.0","id":"req-1","method":"tools/list","params":{}}'
+    scope: Scope = {
+        "type": "http",
+        "method": "POST",
+        "path": "/",
+        "query_string": b"",
+        "headers": [
+            (b"accept", b"application/json, text/event-stream"),
+            (b"content-type", b"application/json"),
+            (b"mcp-protocol-version", b"2025-11-25"),
+        ],
+    }
+    body_sent = False
+
+    async def receive() -> Message:
+        nonlocal body_sent
+        if not body_sent:
+            body_sent = True
+            return {"type": "http.request", "body": body, "more_body": False}
+        raise NotImplementedError
+
+    sent: list[Message] = []
+
+    async def asgi_send(message: Message) -> None:
+        sent.append(message)
+
+    async with transport.connect() as (read_stream, _write_stream):
+        # Model the crashed-session teardown: the read stream the POST handler would
+        # send the wrapped error into is already closed before the handler runs.
+        await read_stream.aclose()
+        # Must not raise out of the ASGI app despite the closed stream.
+        await transport.handle_request(scope, receive, asgi_send)
+
+    assert sent[0]["type"] == "http.response.start"
+    assert sent[0]["status"] == 500
+    body = b"".join(m.get("body", b"") for m in sent if m["type"] == "http.response.body")
+    assert b"backend unavailable" not in body