diff --git a/compiler/src/dotty/tools/dotc/transform/SyntheticMembers.scala b/compiler/src/dotty/tools/dotc/transform/SyntheticMembers.scala
index 45606b0dbef5..040301273d56 100644
--- a/compiler/src/dotty/tools/dotc/transform/SyntheticMembers.scala
+++ b/compiler/src/dotty/tools/dotc/transform/SyntheticMembers.scala
@@ -419,7 +419,13 @@ class SyntheticMembers(thisPhase: DenotTransformer) {
      *
      *  `@unchecked` is needed for parametric case classes.
      */
-    def canEqualBody(that: Tree, span: Span): Tree = that.isInstance(AnnotatedType(clazzType, Annotation(defn.UncheckedAnnot, span)))
+    def canEqualBody(that: Tree, span: Span): Tree = {
+      val clazzTypeU = AnnotatedType(clazzType, Annotation(defn.UncheckedAnnot, span))
+      that.isInstance(clazzTypeU).and(
+        This(clazz).select(defn.Product_productPrefix)
+          .select(defn.Any_==)
+          .appliedTo(that.cast(clazzTypeU).select(defn.Product_productPrefix)))
+    }
 
     symbolsToSynthesize.flatMap(syntheticDefIfMissing)
   }
diff --git a/tests/run/t13033.scala b/tests/run/t13033.scala
new file mode 100644
index 000000000000..c9633677c5b8
--- /dev/null
+++ b/tests/run/t13033.scala
@@ -0,0 +1,24 @@
+case class C(x: Int)
+class D extends C(1) { override def productPrefix = "D" }
+
+abstract case class C1(a: Int)
+class C2(a: Int) extends C1(a) { override def productPrefix = "C2" }
+class C3(a: Int) extends C1(a) { override def productPrefix = "C3" }
+
+case class VCC(x: Int) extends AnyVal
+
+object Test extends App {
+  val c = C(1)
+  assert(c != new D)
+  assert(c == C(1))
+  assert(!c.canEqual(new D))
+
+  val c2 = new C2(1)
+  val c3 = new C3(1)
+  assert(c2 != c3)
+  assert(c2.hashCode != c3.hashCode)
+  assert(!c2.canEqual(c3))
+
+  assert(VCC(1).canEqual(VCC(1)))
+  assert(!VCC(1).canEqual(1))
+}