diff --git a/spec/unit/matrix-client.spec.ts b/spec/unit/matrix-client.spec.ts
index 9a2ae6c97..4756544f3 100644
--- a/spec/unit/matrix-client.spec.ts
+++ b/spec/unit/matrix-client.spec.ts
@@ -417,7 +417,7 @@ describe("MatrixClient", function () {
             ]);
         });
 
-        it("should fallback to unstable endpoint when no support for stable endpoint", async () => {
+        it("should fallback to unstable endpoint when stable endpoint 404s", async () => {
             await assertRequestsMade([
                 {
                     prefix: ClientPrefix.V1,
@@ -433,6 +433,22 @@ describe("MatrixClient", function () {
             ]);
         });
 
+        it("should fallback to unstable endpoint when stable endpoint 405s", async () => {
+            await assertRequestsMade([
+                {
+                    prefix: ClientPrefix.V1,
+                    error: {
+                        httpStatus: 405,
+                        errcode: "M_UNRECOGNIZED",
+                    },
+                },
+                {
+                    prefix: unstableMSC3030Prefix,
+                    data: { event_id: eventId },
+                },
+            ]);
+        });
+
         it("should not fallback to unstable endpoint when stable endpoint returns an error", async () => {
             await assertRequestsMade(
                 [
diff --git a/src/client.ts b/src/client.ts
index e36ef7c41..7ec959299 100644
--- a/src/client.ts
+++ b/src/client.ts
@@ -9391,7 +9391,10 @@ export class MatrixClient extends TypedEventEmitter<EmittedEvents, ClientEventHa
                 ((<MatrixError>err).httpStatus === 400 ||
                     // This the correct standard status code for an unsupported
                     // endpoint according to MSC3743.
-                    (<MatrixError>err).httpStatus === 404)
+                    (<MatrixError>err).httpStatus === 404 ||
+                    // This the correct standard status code for an invalid
+                    // method according to MSC3743.
+                    (<MatrixError>err).httpStatus === 405)
             ) {
                 return await this.http.authedRequest(Method.Get, path, queryParams, undefined, {
                     prefix: "/_matrix/client/unstable/org.matrix.msc3030",