diff --git a/netbox/core/models/jobs.py b/netbox/core/models/jobs.py
index c45b38770..ca7439128 100644
--- a/netbox/core/models/jobs.py
+++ b/netbox/core/models/jobs.py
@@ -11,7 +11,7 @@ from django.core.exceptions import ValidationError
 from django.core.serializers.json import DjangoJSONEncoder
 from django.core.validators import MinValueValidator
 from django.db import models, transaction
-from django.db.models import ExpressionWrapper, F
+from django.db.models import Case, ExpressionWrapper, F, When
 from django.db.models.functions import Coalesce, Now
 from django.urls import reverse
 from django.utils import timezone
@@ -200,11 +200,19 @@ class Job(models.Model):
     def elapsed_time_expression():
         """
         A queryset expression mirroring the `elapsed_time` property, for use in ordering and
-        filtering. Resolves to null for jobs which have not yet started.
+        filtering. Resolves to null for jobs which have not yet started, and for jobs which have
+        completed without recording an execution time.
         """
         return Coalesce(
             'execution_time',
-            ExpressionWrapper(Now() - F('started'), output_field=models.DurationField()),
+            # Only a job which has yet to complete accrues elapsed time
+            Case(
+                When(
+                    completed__isnull=True,
+                    then=ExpressionWrapper(Now() - F('started'), output_field=models.DurationField()),
+                ),
+                output_field=models.DurationField(),
+            ),
         )
 
     def delete(self, *args, **kwargs):
diff --git a/netbox/core/tests/test_models.py b/netbox/core/tests/test_models.py
index bf1f169a1..ce275364b 100644
--- a/netbox/core/tests/test_models.py
+++ b/netbox/core/tests/test_models.py
@@ -418,6 +418,20 @@ class JobTestCase(TestCase):
         self.assertIsNone(job.started)
         self.assertIsNone(job.elapsed_time)
 
+    def test_elapsed_time_none_when_completed_without_execution_time(self):
+        """
+        A job which completed without recording an execution time (e.g. one predating the field)
+        has no elapsed time to report; it must not accrue time indefinitely.
+        """
+        job = self._make_job(None, JobNotificationChoices.NOTIFICATION_NEVER)
+        job.started = timezone.now() - timedelta(seconds=90)
+        job.completed = timezone.now()
+        job.status = JobStatusChoices.STATUS_COMPLETED
+        job.save()
+
+        self.assertIsNone(job.execution_time)
+        self.assertIsNone(job.elapsed_time)
+
     def test_elapsed_time_expression_matches_property(self):
         """
         The elapsed_time_expression() queryset expression should agree with the elapsed_time
@@ -430,6 +444,14 @@ class JobTestCase(TestCase):
         completed.status = JobStatusChoices.STATUS_COMPLETED
         completed.save()
 
+        # A job which completed without recording an execution time must resolve to null, rather
+        # than to an ever-growing interval since it started
+        unrecorded = self._make_job(None, JobNotificationChoices.NOTIFICATION_NEVER)
+        unrecorded.started = timezone.now() - timedelta(seconds=90)
+        unrecorded.completed = timezone.now()
+        unrecorded.status = JobStatusChoices.STATUS_COMPLETED
+        unrecorded.save()
+
         running = self._make_job(None, JobNotificationChoices.NOTIFICATION_NEVER)
         running.started = timezone.now() - timedelta(minutes=5)
         running.save()
@@ -444,6 +466,7 @@ class JobTestCase(TestCase):
         }
 
         self.assertEqual(annotated[completed.pk].elapsed, timedelta(seconds=90))
+        self.assertIsNone(annotated[unrecorded.pk].elapsed)
         self.assertIsNone(annotated[pending.pk].elapsed)
         # The running job's elapsed time is computed at query time, so compare approximately
         self.assertAlmostEqual(