diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8a3bd4e57096..c38f1fd3dc9f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -25,6 +25,8 @@ BUG FIXES:
    be stored [GH-3372]
  * core: Fix issue where node-drain with complete batch allocation would create
    replacement [GH-3217]
+ * core: Allow batch jobs that have been purged to be rerun without a job
+   specification change [GH-3375]
  * core: Fix issue in which batch allocations from previous job versions may not
    have been stopped properly. [GH-3217]
  * core: Fix issue in which allocations with the same name during a scale
diff --git a/scheduler/reconcile.go b/scheduler/reconcile.go
index dc18b17acd92..a94e0462ec16 100644
--- a/scheduler/reconcile.go
+++ b/scheduler/reconcile.go
@@ -500,7 +500,8 @@ func (a *allocReconciler) batchFiltration(all allocSet) (filtered, ignore allocS
 
 	// Ignore terminal batch jobs from older versions
 	for id, alloc := range filtered {
-		if alloc.Job.Version < a.job.Version && alloc.TerminalStatus() {
+		older := alloc.Job.Version < a.job.Version || alloc.Job.CreateIndex < a.job.CreateIndex
+		if older && alloc.TerminalStatus() {
 			delete(filtered, id)
 			ignored[id] = alloc
 		}
diff --git a/scheduler/reconcile_test.go b/scheduler/reconcile_test.go
index c7dcb58e49ba..79d8a8b3dab8 100644
--- a/scheduler/reconcile_test.go
+++ b/scheduler/reconcile_test.go
@@ -3102,3 +3102,49 @@ func TestReconciler_RollingUpgrade_MissingAllocs(t *testing.T) {
 	assertNamesHaveIndexes(t, intRange(7, 9), placeResultsToNames(r.place))
 	assertNamesHaveIndexes(t, intRange(0, 0), destructiveResultsToNames(r.destructiveUpdate))
 }
+
+// Tests that the reconciler handles rerunning a batch job in the case that the
+// allocations are from an older instance of the job.
+func TestReconciler_Batch_Rerun(t *testing.T) {
+	job := mock.Job()
+	job.Type = structs.JobTypeBatch
+	job.TaskGroups[0].Update = nil
+
+	// Create 10 allocations from the old job and have them be complete
+	var allocs []*structs.Allocation
+	for i := 0; i < 10; i++ {
+		alloc := mock.Alloc()
+		alloc.Job = job
+		alloc.JobID = job.ID
+		alloc.NodeID = uuid.Generate()
+		alloc.Name = structs.AllocName(job.ID, job.TaskGroups[0].Name, uint(i))
+		alloc.TaskGroup = job.TaskGroups[0].Name
+		alloc.ClientStatus = structs.AllocClientStatusComplete
+		alloc.DesiredStatus = structs.AllocDesiredStatusStop
+		allocs = append(allocs, alloc)
+	}
+
+	// Create a copy of the job that is "new"
+	job2 := job.Copy()
+	job2.CreateIndex++
+
+	reconciler := NewAllocReconciler(testLogger(), allocUpdateFnIgnore, true, job2.ID, job2, nil, allocs, nil)
+	r := reconciler.Compute()
+
+	// Assert the correct results
+	assertResults(t, r, &resultExpectation{
+		createDeployment:  nil,
+		deploymentUpdates: nil,
+		place:             10,
+		destructive:       0,
+		desiredTGUpdates: map[string]*structs.DesiredUpdates{
+			job.TaskGroups[0].Name: {
+				Place:             10,
+				DestructiveUpdate: 0,
+				Ignore:            10,
+			},
+		},
+	})
+
+	assertNamesHaveIndexes(t, intRange(0, 9), placeResultsToNames(r.place))
+}