diff --git a/clientconn.go b/clientconn.go
index 5dec2dacc0ba..ed98d5072bbe 100644
--- a/clientconn.go
+++ b/clientconn.go
@@ -323,7 +323,7 @@ func DialContext(ctx context.Context, target string, opts ...DialOption) (conn *
 			case err == nil || !cc.dopts.returnLastError:
 				conn, err = nil, ctx.Err()
 			default:
-				conn, err = nil, fmt.Errorf("%v: %v", ctx.Err(), err)
+				conn, err = nil, fmt.Errorf("%v: %w", err, ctx.Err())
 			}
 		default:
 		}
diff --git a/dial_test.go b/dial_test.go
index 7b74aac79fa6..79a87a8dbc5f 100644
--- a/dial_test.go
+++ b/dial_test.go
@@ -20,6 +20,7 @@ package grpc
 
 import (
 	"context"
+	"errors"
 	"fmt"
 	"net"
 	"strings"
@@ -162,7 +163,11 @@ func (s) TestDialWaitsForServerSettingsAndFails(t *testing.T) {
 		client.Close()
 		t.Fatalf("Unexpected success (err=nil) while dialing")
 	}
-	expectedMsg := "server preface"
+	// The error should wrap context.DeadlineExceeded.
+	if !errors.Is(err, context.DeadlineExceeded) {
+		t.Errorf("DialContext() returned %v, want %v", err, context.DeadlineExceeded)
+	}
+	const expectedMsg = "error reading server preface"
 	if !strings.Contains(err.Error(), context.DeadlineExceeded.Error()) || !strings.Contains(err.Error(), expectedMsg) {
 		t.Fatalf("DialContext(_) = %v; want a message that includes both %q and %q", err, context.DeadlineExceeded.Error(), expectedMsg)
 	}