diff --git a/src/main/java/org/kohsuke/github/extras/okhttp3/ObsoleteUrlFactory.java b/src/main/java/org/kohsuke/github/extras/okhttp3/ObsoleteUrlFactory.java
index 0849a7409..54091b42c 100644
--- a/src/main/java/org/kohsuke/github/extras/okhttp3/ObsoleteUrlFactory.java
+++ b/src/main/java/org/kohsuke/github/extras/okhttp3/ObsoleteUrlFactory.java
@@ -14,6 +14,7 @@ import okhttp3.Protocol;
 import okhttp3.Request;
 import okhttp3.RequestBody;
 import okhttp3.Response;
+import okhttp3.ResponseBody;
 import okio.Buffer;
 import okio.BufferedSink;
 import okio.Okio;
@@ -179,7 +180,7 @@ public final class ObsoleteUrlFactory implements URLStreamHandlerFactory, Clonea
      * <p>
      * This code configures OkHttp to handle all HTTP and HTTPS connections created with
      * {@link java.net.URL#openConnection()}:
-     * 
+     *
      * <pre>
      * {
      *     &#64;code
@@ -404,7 +405,7 @@ public final class ObsoleteUrlFactory implements URLStreamHandlerFactory, Clonea
             try {
                 Response response = getResponse(true);
                 if (hasBody(response) && response.code() >= HTTP_BAD_REQUEST) {
-                    return response.body().byteStream();
+                    return new ResponseBodyInputStream(response.body());
                 }
                 return null;
             } catch (IOException e) {
@@ -486,7 +487,7 @@ public final class ObsoleteUrlFactory implements URLStreamHandlerFactory, Clonea
             Response response = getResponse(false);
             if (response.code() >= HTTP_BAD_REQUEST)
                 throw new FileNotFoundException(url.toString());
-            return response.body().byteStream();
+            return new ResponseBodyInputStream(response.body());
         }
 
         @Override
@@ -957,6 +958,7 @@ public final class ObsoleteUrlFactory implements URLStreamHandlerFactory, Clonea
             initOutputStream(Okio.buffer(pipe.sink()), expectedContentLength);
         }
 
+        @Override
         public boolean isOneShot() {
             return true;
         }
@@ -1367,4 +1369,69 @@ public final class ObsoleteUrlFactory implements URLStreamHandlerFactory, Clonea
             super(cause);
         }
     }
+
+    /**
+     * Make sure both the ResponseBody and the InputStream are closed when the InputStream coming from the ResponseBody
+     * is closed.
+     */
+    private static final class ResponseBodyInputStream extends InputStream {
+
+        private final ResponseBody responseBody;
+
+        private final InputStream inputStream;
+
+        private ResponseBodyInputStream(ResponseBody responseBody) {
+            this.responseBody = responseBody;
+            this.inputStream = responseBody.byteStream();
+        }
+
+        @Override
+        public int read() throws IOException {
+            return inputStream.read();
+        }
+
+        @Override
+        public int read(byte b[]) throws IOException {
+            return inputStream.read(b);
+        }
+
+        @Override
+        public int read(byte b[], int off, int len) throws IOException {
+            return inputStream.read(b, off, len);
+        }
+
+        @Override
+        public long skip(long n) throws IOException {
+            return inputStream.skip(n);
+        }
+
+        @Override
+        public int available() throws IOException {
+            return inputStream.available();
+        }
+
+        @Override
+        public synchronized void mark(int readlimit) {
+            inputStream.mark(readlimit);
+        }
+
+        @Override
+        public synchronized void reset() throws IOException {
+            inputStream.reset();
+        }
+
+        @Override
+        public boolean markSupported() {
+            return inputStream.markSupported();
+        }
+
+        @Override
+        public void close() throws IOException {
+            try {
+                inputStream.close();
+            } finally {
+                responseBody.close();
+            }
+        }
+    }
 }