diff --git a/datafusion/physical-plan/src/sorts/cursor.rs b/datafusion/physical-plan/src/sorts/cursor.rs
index 17033e6a31425..89fbb0fbcf89e 100644
--- a/datafusion/physical-plan/src/sorts/cursor.rs
+++ b/datafusion/physical-plan/src/sorts/cursor.rs
@@ -16,6 +16,7 @@
 // under the License.
 
 use std::cmp::Ordering;
+use std::sync::Arc;
 
 use arrow::array::{
     types::ByteArrayType, Array, ArrowPrimitiveType, GenericByteArray,
@@ -151,7 +152,7 @@ impl<T: CursorValues> Ord for Cursor<T> {
 /// Used for sorting when there are multiple columns in the sort key
 #[derive(Debug)]
 pub struct RowValues {
-    rows: Rows,
+    rows: Arc<Rows>,
 
     /// Tracks for the memory used by in the `Rows` of this
     /// cursor. Freed on drop
@@ -164,7 +165,7 @@ impl RowValues {
     ///
     /// Panics if the reservation is not for exactly `rows.size()`
     /// bytes or if `rows` is empty.
-    pub fn new(rows: Rows, reservation: MemoryReservation) -> Self {
+    pub fn new(rows: Arc<Rows>, reservation: MemoryReservation) -> Self {
         assert_eq!(
             rows.size(),
             reservation.size(),
diff --git a/datafusion/physical-plan/src/sorts/stream.rs b/datafusion/physical-plan/src/sorts/stream.rs
index e029c60b285b6..49e7413122fca 100644
--- a/datafusion/physical-plan/src/sorts/stream.rs
+++ b/datafusion/physical-plan/src/sorts/stream.rs
@@ -21,8 +21,8 @@ use crate::{PhysicalExpr, PhysicalSortExpr};
 use arrow::array::Array;
 use arrow::datatypes::Schema;
 use arrow::record_batch::RecordBatch;
-use arrow::row::{RowConverter, SortField};
-use datafusion_common::Result;
+use arrow::row::{RowConverter, Rows, SortField};
+use datafusion_common::{internal_datafusion_err, Result};
 use datafusion_execution::memory_pool::MemoryReservation;
 use datafusion_physical_expr_common::sort_expr::LexOrdering;
 use futures::stream::{Fuse, StreamExt};
@@ -76,8 +76,40 @@ impl FusedStreams {
     }
 }
 
+/// A pair of `Arc<Rows>` that can be reused
+#[derive(Debug)]
+struct ReusableRows {
+    // inner[stream_idx] holds a two Arcs:
+    // at start of a new poll
+    // .0 is the rows from the previous poll (at start),
+    // .1 is the one that is being written to
+    // at end of a poll, .0 will be swapped with .1,
+    inner: Vec<[Option<Arc<Rows>>; 2]>,
+}
+
+impl ReusableRows {
+    // return a Rows for writing,
+    // does not clone if the existing rows can be reused
+    fn take_next(&mut self, stream_idx: usize) -> Result<Rows> {
+        Arc::try_unwrap(self.inner[stream_idx][1].take().unwrap()).map_err(|_| {
+            internal_datafusion_err!(
+                "Rows from RowCursorStream is still in use by consumer"
+            )
+        })
+    }
+    // save the Rows
+    fn save(&mut self, stream_idx: usize, rows: Arc<Rows>) {
+        self.inner[stream_idx][1] = Some(Arc::clone(&rows));
+        // swap the curent with the previous one, so that the next poll can reuse the Rows from the previous poll
+        let [a, b] = &mut self.inner[stream_idx];
+        std::mem::swap(a, b);
+    }
+}
+
 /// A [`PartitionedStream`] that wraps a set of [`SendableRecordBatchStream`]
 /// and computes [`RowValues`] based on the provided [`PhysicalSortExpr`]
+/// Note: the stream returns an error if the consumer buffers more than one RowValues (i.e. holds on to two RowValues
+/// from the same partition at the same time).
 #[derive(Debug)]
 pub struct RowCursorStream {
     /// Converter to convert output of physical expressions
@@ -88,6 +120,9 @@ pub struct RowCursorStream {
     streams: FusedStreams,
     /// Tracks the memory used by `converter`
     reservation: MemoryReservation,
+    /// Allocated rows for each partition, we keep two to allow for buffering one
+    /// in the consumer of the stream
+    rows: ReusableRows,
 }
 
 impl RowCursorStream {
@@ -105,26 +140,48 @@ impl RowCursorStream {
             })
             .collect::<Result<Vec<_>>>()?;
 
-        let streams = streams.into_iter().map(|s| s.fuse()).collect();
+        let streams: Vec<_> = streams.into_iter().map(|s| s.fuse()).collect();
         let converter = RowConverter::new(sort_fields)?;
+        let mut rows = Vec::with_capacity(streams.len());
+        for _ in &streams {
+            // Initialize each stream with an empty Rows
+            rows.push([
+                Some(Arc::new(converter.empty_rows(0, 0))),
+                Some(Arc::new(converter.empty_rows(0, 0))),
+            ]);
+        }
         Ok(Self {
             converter,
             reservation,
             column_expressions: expressions.iter().map(|x| Arc::clone(&x.expr)).collect(),
             streams: FusedStreams(streams),
+            rows: ReusableRows { inner: rows },
         })
     }
 
-    fn convert_batch(&mut self, batch: &RecordBatch) -> Result<RowValues> {
+    fn convert_batch(
+        &mut self,
+        batch: &RecordBatch,
+        stream_idx: usize,
+    ) -> Result<RowValues> {
         let cols = self
             .column_expressions
             .iter()
             .map(|expr| expr.evaluate(batch)?.into_array(batch.num_rows()))
             .collect::<Result<Vec<_>>>()?;
 
-        let rows = self.converter.convert_columns(&cols)?;
+        // At this point, ownership should of this Rows should be unique
+        let mut rows = self.rows.take_next(stream_idx)?;
+
+        rows.clear();
+
+        self.converter.append(&mut rows, &cols)?;
         self.reservation.try_resize(self.converter.size())?;
 
+        let rows = Arc::new(rows);
+
+        self.rows.save(stream_idx, Arc::clone(&rows));
+
         // track the memory in the newly created Rows.
         let mut rows_reservation = self.reservation.new_empty();
         rows_reservation.try_grow(rows.size())?;
@@ -146,7 +203,7 @@ impl PartitionedStream for RowCursorStream {
     ) -> Poll<Option<Self::Output>> {
         Poll::Ready(ready!(self.streams.poll_next(cx, stream_idx)).map(|r| {
             r.and_then(|batch| {
-                let cursor = self.convert_batch(&batch)?;
+                let cursor = self.convert_batch(&batch, stream_idx)?;
                 Ok((cursor, batch))
             })
         }))