diff --git a/datafusion/expr/src/logical_plan/plan.rs b/datafusion/expr/src/logical_plan/plan.rs
index 6d4c57c5c4c0..a354fb666f99 100644
--- a/datafusion/expr/src/logical_plan/plan.rs
+++ b/datafusion/expr/src/logical_plan/plan.rs
@@ -2503,9 +2503,22 @@ impl Window {
 // Manual implementation needed because of `schema` field. Comparison excludes this field.
 impl PartialOrd for Window {
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        match self.input.partial_cmp(&other.input) {
-            Some(Ordering::Equal) => self.window_expr.partial_cmp(&other.window_expr),
-            cmp => cmp,
+        match self.input.partial_cmp(&other.input)? {
+            Ordering::Equal => {} // continue
+            not_equal => return Some(not_equal),
+        }
+
+        match self.window_expr.partial_cmp(&other.window_expr)? {
+            Ordering::Equal => {} // continue
+            not_equal => return Some(not_equal),
+        }
+
+        // Contract for PartialOrd and PartialEq consistency requires that
+        // a == b if and only if partial_cmp(a, b) == Some(Equal).
+        if self == other {
+            Some(Ordering::Equal)
+        } else {
+            None
         }
     }
 }
@@ -4268,22 +4281,20 @@ fn get_unnested_list_datatype_recursive(
 
 #[cfg(test)]
 mod tests {
-
     use super::*;
     use crate::builder::LogicalTableSource;
     use crate::logical_plan::table_scan;
+    use crate::test::function_stub::{count, count_udaf};
     use crate::{
         binary_expr, col, exists, in_subquery, lit, placeholder, scalar_subquery,
         GroupingSet,
     };
-
     use datafusion_common::tree_node::{
         TransformedResult, TreeNodeRewriter, TreeNodeVisitor,
     };
     use datafusion_common::{not_impl_err, Constraint, ScalarValue};
     use insta::{assert_debug_snapshot, assert_snapshot};
-
-    use crate::test::function_stub::count;
+    use std::hash::DefaultHasher;
 
     fn employee_schema() -> Schema {
         Schema::new(vec![
@@ -4687,6 +4698,63 @@ mod tests {
         );
     }
 
+    #[test]
+    fn test_partial_eq_hash_and_partial_ord() {
+        let empty_values = Arc::new(LogicalPlan::EmptyRelation(EmptyRelation {
+            produce_one_row: true,
+            schema: Arc::new(DFSchema::empty()),
+        }));
+
+        let count_window_function = |schema| {
+            Window::try_new_with_schema(
+                vec![Expr::WindowFunction(Box::new(WindowFunction::new(
+                    WindowFunctionDefinition::AggregateUDF(count_udaf()),
+                    vec![],
+                )))],
+                Arc::clone(&empty_values),
+                Arc::new(schema),
+            )
+            .unwrap()
+        };
+
+        let schema_without_metadata = || {
+            DFSchema::from_unqualified_fields(
+                vec![Field::new("count", DataType::Int64, false)].into(),
+                HashMap::new(),
+            )
+            .unwrap()
+        };
+
+        let schema_with_metadata = || {
+            DFSchema::from_unqualified_fields(
+                vec![Field::new("count", DataType::Int64, false)].into(),
+                [("key".to_string(), "value".to_string())].into(),
+            )
+            .unwrap()
+        };
+
+        // A Window
+        let f = count_window_function(schema_without_metadata());
+
+        // Same like `f`, different instance
+        let f2 = count_window_function(schema_without_metadata());
+        assert_eq!(f, f2);
+        assert_eq!(hash(&f), hash(&f2));
+        assert_eq!(f.partial_cmp(&f2), Some(Ordering::Equal));
+
+        // Same like `f`, except for schema metadata
+        let o = count_window_function(schema_with_metadata());
+        assert_ne!(f, o);
+        assert_ne!(hash(&f), hash(&o)); // hash can collide for different values but does not collide in this test
+        assert_eq!(f.partial_cmp(&o), None);
+    }
+
+    fn hash<T: Hash>(value: &T) -> u64 {
+        let hasher = &mut DefaultHasher::new();
+        value.hash(hasher);
+        hasher.finish()
+    }
+
     #[test]
     fn projection_expr_schema_mismatch() -> Result<()> {
         let empty_schema = Arc::new(DFSchema::empty());