diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index 9a119c633..fdd024b7d 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -236,20 +236,25 @@ async def _handle_resumption_request(self, ctx: RequestContext) -> None:
         if isinstance(ctx.session_message.message, JSONRPCRequest):  # pragma: no branch
             original_request_id = ctx.session_message.message.id
 
-        async with aconnect_sse(ctx.client, "GET", self.url, headers=headers) as event_source:
-            event_source.response.raise_for_status()
-            logger.debug("Resumption GET SSE connection established")
+        event_source: EventSource | None = None
+        try:
+            async with aconnect_sse(ctx.client, "GET", self.url, headers=headers) as es:
+                event_source = es
+                event_source.response.raise_for_status()
+                logger.debug("Resumption GET SSE connection established")
 
-            async for sse in event_source.aiter_sse():  # pragma: no branch
-                is_complete = await self._handle_sse_event(
-                    sse,
-                    ctx.read_stream_writer,
-                    original_request_id,
-                    ctx.metadata.on_resumption_token_update if ctx.metadata else None,
-                )
-                if is_complete:
-                    await event_source.response.aclose()
-                    break
+                async for sse in event_source.aiter_sse():  # pragma: no branch
+                    is_complete = await self._handle_sse_event(
+                        sse,
+                        ctx.read_stream_writer,
+                        original_request_id,
+                        ctx.metadata.on_resumption_token_update if ctx.metadata else None,
+                    )
+                    if is_complete:
+                        break
+        finally:
+            if event_source is not None:  # pragma: no branch
+                await event_source.response.aclose()
 
     async def _handle_post_request(self, ctx: RequestContext) -> None:
         """Handle a POST request with response processing."""
@@ -361,10 +366,11 @@ async def _handle_sse_response(
                 # If the SSE event indicates completion, like returning response/error
                 # break the loop
                 if is_complete:
-                    await response.aclose()
                     return  # Normal completion, no reconnect needed
         except Exception:
-            logger.debug("SSE stream ended", exc_info=True)  # pragma: no cover
+            logger.debug("SSE stream ended", exc_info=True)
+        finally:
+            await response.aclose()
 
         # Stream ended without response - reconnect if we received an event with ID
         if last_event_id is not None:  # pragma: no branch
diff --git a/tests/client/test_streamable_http_response_cleanup.py b/tests/client/test_streamable_http_response_cleanup.py
new file mode 100644
index 000000000..0fa4ede44
--- /dev/null
+++ b/tests/client/test_streamable_http_response_cleanup.py
@@ -0,0 +1,128 @@
+import contextlib
+
+import httpx
+import pytest
+from httpx_sse import ServerSentEvent
+
+from mcp.client.streamable_http import RequestContext, StreamableHTTPTransport
+from mcp.shared._context_streams import create_context_streams
+from mcp.shared.message import ClientMessageMetadata, SessionMessage
+from mcp.types import JSONRPCRequest
+
+
+class _RaiseEventSource:
+    def __init__(self, response: httpx.Response) -> None:
+        self.response = response
+
+    async def aiter_sse(self):
+        yield ServerSentEvent(event="message", data="", id=None, retry=None)
+        raise RuntimeError("boom")
+
+
+@pytest.mark.anyio
+async def test_handle_sse_response_closes_response_on_exception(monkeypatch: pytest.MonkeyPatch) -> None:
+    closed = False
+
+    async def spy_aclose() -> None:
+        nonlocal closed
+        closed = True
+
+    response = httpx.Response(200, headers={"content-type": "text/event-stream"})
+    response.aclose = spy_aclose  # type: ignore[method-assign]
+
+    monkeypatch.setattr("mcp.client.streamable_http.EventSource", _RaiseEventSource)
+
+    send_stream, receive_stream = create_context_streams[SessionMessage | Exception](1)
+    async with send_stream, receive_stream:
+        transport = StreamableHTTPTransport("http://example.invalid/mcp")
+        async with httpx.AsyncClient(transport=httpx.MockTransport(lambda _: httpx.Response(200))) as client:
+            ctx = RequestContext(
+                client=client,
+                session_id=None,
+                session_message=SessionMessage(JSONRPCRequest(method="initialize", params={}, jsonrpc="2.0", id=1)),
+                metadata=ClientMessageMetadata(),
+                read_stream_writer=send_stream,
+            )
+            await transport._handle_sse_response(response, ctx)
+
+    assert closed
+
+
+@pytest.mark.anyio
+async def test_handle_resumption_request_closes_response_when_aconnect_sse_raises(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    @contextlib.asynccontextmanager
+    async def fake_aconnect_sse(*_args: object, **_kwargs: object):
+        raise RuntimeError("connect failed")
+        yield
+
+    monkeypatch.setattr("mcp.client.streamable_http.aconnect_sse", fake_aconnect_sse)
+
+    send_stream, receive_stream = create_context_streams[SessionMessage | Exception](1)
+    async with send_stream, receive_stream:
+        transport = StreamableHTTPTransport("http://example.invalid/mcp")
+        metadata = ClientMessageMetadata(resumption_token="1")
+        async with httpx.AsyncClient(transport=httpx.MockTransport(lambda _: httpx.Response(200))) as client:
+            ctx = RequestContext(
+                client=client,
+                session_id=None,
+                session_message=SessionMessage(JSONRPCRequest(method="initialize", params={}, jsonrpc="2.0", id=1)),
+                metadata=metadata,
+                read_stream_writer=send_stream,
+            )
+
+            error: RuntimeError | None = None
+            try:
+                await transport._handle_resumption_request(ctx)
+            except RuntimeError as exc:
+                error = exc
+
+            assert error is not None
+            assert str(error) == "connect failed"
+
+
+@pytest.mark.anyio
+async def test_handle_resumption_request_closes_response_on_exception(monkeypatch: pytest.MonkeyPatch) -> None:
+    closed = False
+
+    async def spy_aclose() -> None:
+        nonlocal closed
+        closed = True
+
+    response = httpx.Response(
+        200,
+        headers={"content-type": "text/event-stream"},
+        request=httpx.Request("GET", "http://example.invalid/mcp"),
+    )
+    response.aclose = spy_aclose  # type: ignore[method-assign]
+
+    @contextlib.asynccontextmanager
+    async def fake_aconnect_sse(*_args: object, **_kwargs: object):
+        yield _RaiseEventSource(response)
+
+    monkeypatch.setattr("mcp.client.streamable_http.aconnect_sse", fake_aconnect_sse)
+
+    send_stream, receive_stream = create_context_streams[SessionMessage | Exception](1)
+    async with send_stream, receive_stream:
+        transport = StreamableHTTPTransport("http://example.invalid/mcp")
+        metadata = ClientMessageMetadata(resumption_token="1")
+        async with httpx.AsyncClient(transport=httpx.MockTransport(lambda _: httpx.Response(200))) as client:
+            ctx = RequestContext(
+                client=client,
+                session_id=None,
+                session_message=SessionMessage(JSONRPCRequest(method="initialize", params={}, jsonrpc="2.0", id=1)),
+                metadata=metadata,
+                read_stream_writer=send_stream,
+            )
+
+            error: RuntimeError | None = None
+            try:
+                await transport._handle_resumption_request(ctx)
+            except RuntimeError as exc:
+                error = exc
+
+            assert error is not None
+            assert str(error) == "boom"
+
+    assert closed