diff --git a/datafusion/physical-plan/src/sorts/sort.rs b/datafusion/physical-plan/src/sorts/sort.rs
index e7e1c5481f80..a81b09948cca 100644
--- a/datafusion/physical-plan/src/sorts/sort.rs
+++ b/datafusion/physical-plan/src/sorts/sort.rs
@@ -499,6 +499,12 @@ impl ExternalSorter {
         metrics: BaselineMetrics,
     ) -> Result<SendableRecordBatchStream> {
         assert_ne!(self.in_mem_batches.len(), 0);
+
+        // The elapsed compute timer is updated when the value is dropped.
+        // There is no need for an explicit call to drop.
+        let elapsed_compute = metrics.elapsed_compute().clone();
+        let _timer = elapsed_compute.timer();
+
         if self.in_mem_batches.len() == 1 {
             let batch = self.in_mem_batches.remove(0);
             let reservation = self.reservation.take();
@@ -552,7 +558,9 @@ impl ExternalSorter {
         let fetch = self.fetch;
         let expressions = Arc::clone(&self.expr);
         let stream = futures::stream::once(futures::future::lazy(move |_| {
+            let timer = metrics.elapsed_compute().timer();
             let sorted = sort_batch(&batch, &expressions, fetch)?;
+            timer.done();
             metrics.record_output(sorted.num_rows());
             drop(batch);
             drop(reservation);