diff --git a/pgconn/errors.go b/pgconn/errors.go
index bc1e31e31..5d90ad2ba 100644
--- a/pgconn/errors.go
+++ b/pgconn/errors.go
@@ -144,7 +144,7 @@ func normalizeTimeoutError(ctx context.Context, err error) error {
 		} else if ctx.Err() == context.DeadlineExceeded {
 			return &errTimeout{err: ctx.Err()}
 		} else {
-			return &errTimeout{err: netErr}
+			return &errTimeout{err: err}
 		}
 	}
 	return err
diff --git a/pgconn/pgconn.go b/pgconn/pgconn.go
index abf6c9d8d..45b6362da 100644
--- a/pgconn/pgconn.go
+++ b/pgconn/pgconn.go
@@ -292,7 +292,13 @@ func connectPreferred(ctx context.Context, config *Config, connectOneConfigs []*
 	}
 
 	if fallbackConnectOneConfig != nil {
-		pgConn, err := connectOne(ctx, config, fallbackConnectOneConfig, true)
+		fallbackCtx := octx
+		if config.ConnectTimeout != 0 {
+			var cancel context.CancelFunc
+			fallbackCtx, cancel = context.WithTimeout(octx, config.ConnectTimeout)
+			defer cancel()
+		}
+		pgConn, err := connectOne(fallbackCtx, config, fallbackConnectOneConfig, true)
 		if err == nil {
 			return pgConn, nil
 		}
diff --git a/pgconn/pgconn_private_test.go b/pgconn/pgconn_private_test.go
index a0c15c27a..218071630 100644
--- a/pgconn/pgconn_private_test.go
+++ b/pgconn/pgconn_private_test.go
@@ -1,9 +1,14 @@
 package pgconn
 
 import (
+	"context"
+	"errors"
+	"fmt"
+	"net"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
 func TestCommandTag(t *testing.T) {
@@ -39,3 +44,42 @@ func TestCommandTag(t *testing.T) {
 		assert.Equalf(t, tt.isSelect, ct.Select(), "%d. %v", i, tt.commandTag)
 	}
 }
+
+// timeoutNetError is a net.Error that always reports Timeout() == true.
+type timeoutNetError struct{ msg string }
+
+func (e *timeoutNetError) Error() string   { return e.msg }
+func (e *timeoutNetError) Timeout() bool   { return true }
+func (e *timeoutNetError) Temporary() bool { return false }
+
+// wrappedDialError simulates a DialError wrapping a net.Error, like the error
+// produced when a dial deadline is exceeded on a custom dialer.
+type wrappedDialError struct {
+	addr string
+	err  error
+}
+
+func (e *wrappedDialError) Error() string { return fmt.Sprintf("dial %s: %s", e.addr, e.err) }
+func (e *wrappedDialError) Unwrap() error { return e.err }
+
+func TestNormalizeTimeoutError_PreservesErrorChain(t *testing.T) {
+	t.Parallel()
+
+	inner := &timeoutNetError{msg: "i/o timeout"}
+	outer := &wrappedDialError{addr: "192.0.2.1:5432", err: inner}
+
+	// Sanity check: errors.As finds the net.Error through the wrapper.
+	var netErr net.Error
+	require.True(t, errors.As(outer, &netErr))
+
+	result := normalizeTimeoutError(context.Background(), outer)
+
+	// The result should be an errTimeout and should still unwrap to the
+	// original wrappedDialError so callers can inspect dial context (address, etc.).
+	var te *errTimeout
+	require.True(t, errors.As(result, &te))
+
+	var dial *wrappedDialError
+	assert.True(t, errors.As(result, &dial), "original dial error should be preserved in the chain")
+	assert.Equal(t, "192.0.2.1:5432", dial.addr)
+}