diff --git a/src/response.rs b/src/response.rs
index 38f44f1..a768535 100644
--- a/src/response.rs
+++ b/src/response.rs
@@ -221,6 +221,11 @@ impl Response {
         &self.error
     }
 
+    // Internal-only API, to allow unit::connect to return early on errors.
+    pub(crate) fn into_error(self) -> Option<Error> {
+        self.error
+    }
+
     /// The content type part of the "Content-Type" header without
     /// the charset.
     ///
diff --git a/src/unit.rs b/src/unit.rs
index 3ec4794..0431009 100644
--- a/src/unit.rs
+++ b/src/unit.rs
@@ -181,6 +181,9 @@ pub(crate) fn connect(
     // start reading the response to process cookies and redirects.
     let mut stream = stream::DeadlineStream::new(stream, unit.deadline);
     let mut resp = Response::from_read(&mut stream);
+    if resp.synthetic_error().is_some() {
+        return Err(resp.into_error().unwrap());
+    }
 
     // https://tools.ietf.org/html/rfc7230#section-6.3.1
     // When an inbound connection is closed prematurely, a client MAY