diff --git a/datafusion/functions-aggregate/src/first_last.rs b/datafusion/functions-aggregate/src/first_last.rs
index 8e6bf9205b2f..33387f5d7234 100644
--- a/datafusion/functions-aggregate/src/first_last.rs
+++ b/datafusion/functions-aggregate/src/first_last.rs
@@ -1419,8 +1419,9 @@ mod tests {
 
     use arrow::{
         array::{BooleanArray, Int64Array, ListArray, PrimitiveArray, StringArray},
+        compute,
         compute::SortOptions,
-        datatypes::Schema,
+        datatypes::{Field, Schema},
     };
     use datafusion_physical_expr::{PhysicalSortExpr, expressions::col};
 
@@ -1879,6 +1880,59 @@ mod tests {
         Ok(())
     }
 
+    #[test]
+    fn test_first_value_ordered_update_batch_picks_min_ordering() -> Result<()> {
+        // Verify ordered first_value chooses the row with the smallest ordering key.
+        let mut accumulator = new_first_value_accumulator()?;
+
+        accumulator.update_batch(&[
+            Arc::new(StringArray::from(vec![Some("c"), Some("a"), Some("b")])),
+            Arc::new(Int64Array::from(vec![3, 1, 2])),
+        ])?;
+
+        assert_eq!(accumulator.evaluate()?, ScalarValue::from("a"));
+        Ok(())
+    }
+
+    #[test]
+    fn test_last_value_ordered_update_batch_picks_max_ordering() -> Result<()> {
+        // Verify ordered last_value chooses the row with the largest ordering key.
+        let mut accumulator = new_last_value_accumulator()?;
+
+        accumulator.update_batch(&[
+            Arc::new(StringArray::from(vec![Some("c"), Some("a"), Some("b")])),
+            Arc::new(Int64Array::from(vec![3, 1, 2])),
+        ])?;
+
+        assert_eq!(accumulator.evaluate()?, ScalarValue::from("c"));
+        Ok(())
+    }
+
+    #[test]
+    fn test_first_value_ordered_merge_batch_prefers_earlier_state() -> Result<()> {
+        // Verify merge_batch keeps the earliest value across partial states.
+        let mut lhs = new_first_value_accumulator()?;
+        lhs.update_batch(&[
+            Arc::new(StringArray::from(vec![Some("later")])),
+            Arc::new(Int64Array::from(vec![10])),
+        ])?;
+        let lhs_state = lhs.state()?;
+
+        let mut rhs = new_first_value_accumulator()?;
+        rhs.update_batch(&[
+            Arc::new(StringArray::from(vec![Some("earlier")])),
+            Arc::new(Int64Array::from(vec![1])),
+        ])?;
+        let rhs_state = rhs.state()?;
+
+        let mut merged = new_first_value_accumulator()?;
+        let states = concat_states(&lhs_state, &rhs_state)?;
+        merged.merge_batch(&states)?;
+
+        assert_eq!(merged.evaluate()?, ScalarValue::from("earlier"));
+        Ok(())
+    }
+
     #[test]
     fn test_last_value_merge_with_is_set_nulls() -> Result<()> {
         // Test data with corrupted is_set flag
@@ -1925,4 +1979,69 @@ mod tests {
 
         Ok(())
     }
+
+    #[test]
+    fn test_last_value_ordered_merge_batch_prefers_later_state() -> Result<()> {
+        // Verify merge_batch keeps the latest value across partial states.
+        let mut lhs = new_last_value_accumulator()?;
+        lhs.update_batch(&[
+            Arc::new(StringArray::from(vec![Some("earlier")])),
+            Arc::new(Int64Array::from(vec![1])),
+        ])?;
+        let lhs_state = lhs.state()?;
+
+        let mut rhs = new_last_value_accumulator()?;
+        rhs.update_batch(&[
+            Arc::new(StringArray::from(vec![Some("later")])),
+            Arc::new(Int64Array::from(vec![10])),
+        ])?;
+        let rhs_state = rhs.state()?;
+
+        let mut merged = new_last_value_accumulator()?;
+        let states = concat_states(&lhs_state, &rhs_state)?;
+        merged.merge_batch(&states)?;
+
+        assert_eq!(merged.evaluate()?, ScalarValue::from("later"));
+        Ok(())
+    }
+
+    fn new_first_value_accumulator() -> Result<FirstValueAccumulator> {
+        FirstValueAccumulator::try_new(
+            &DataType::Utf8,
+            &[DataType::Int64],
+            single_ordering()?,
+            false,
+            false,
+        )
+    }
+
+    fn new_last_value_accumulator() -> Result<LastValueAccumulator> {
+        LastValueAccumulator::try_new(
+            &DataType::Utf8,
+            &[DataType::Int64],
+            single_ordering()?,
+            false,
+            false,
+        )
+    }
+
+    fn single_ordering() -> Result<LexOrdering> {
+        let schema = Schema::new(vec![Field::new("ordering", DataType::Int64, false)]);
+        let ordering_expr = col("ordering", &schema)?;
+        Ok(LexOrdering::new(vec![PhysicalSortExpr {
+            expr: ordering_expr,
+            options: SortOptions::default(),
+        }])
+        .unwrap())
+    }
+
+    fn concat_states(lhs: &[ScalarValue], rhs: &[ScalarValue]) -> Result<Vec<ArrayRef>> {
+        assert_eq!(lhs.len(), rhs.len());
+        (0..lhs.len())
+            .map(|idx| {
+                compute::concat(&[&lhs[idx].to_array()?, &rhs[idx].to_array()?])
+                    .map_err(|e| arrow_datafusion_err!(e))
+            })
+            .collect()
+    }
 }