diff --git a/pkg/webhooks/jobset_webhook.go b/pkg/webhooks/jobset_webhook.go
index f6639590..3cdf589f 100644
--- a/pkg/webhooks/jobset_webhook.go
+++ b/pkg/webhooks/jobset_webhook.go
@@ -314,9 +314,9 @@ func (j *jobSetWebhook) ValidateUpdate(ctx context.Context, old, newObj runtime.
 	}
 	mungedSpec := js.Spec.DeepCopy()
 
-	// Allow pod template to be mutated for suspended JobSets.
+	// Allow pod template to be mutated for suspended JobSets, or JobSets getting suspended.
 	// This is needed for integration with Kueue/DWS.
-	if ptr.Deref(oldJS.Spec.Suspend, false) {
+	if ptr.Deref(oldJS.Spec.Suspend, false) || ptr.Deref(js.Spec.Suspend, false) {
 		for index := range js.Spec.ReplicatedJobs {
 			// Pod values which must be mutable for Kueue are defined here: https://github.com/kubernetes-sigs/kueue/blob/a50d395c36a2cb3965be5232162cf1fded1bdb08/apis/kueue/v1beta1/workload_types.go#L256-L260
 			mungedSpec.ReplicatedJobs[index].Template.Spec.Template.Annotations = oldJS.Spec.ReplicatedJobs[index].Template.Spec.Template.Annotations
diff --git a/test/e2e/e2e_test.go b/test/e2e/e2e_test.go
index 8c713a72..19f2a6f2 100644
--- a/test/e2e/e2e_test.go
+++ b/test/e2e/e2e_test.go
@@ -24,6 +24,7 @@ import (
 	corev1 "k8s.io/api/core/v1"
 	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
 	"k8s.io/apimachinery/pkg/types"
+	"k8s.io/utils/ptr"
 
 	jobset "sigs.k8s.io/jobset/api/jobset/v1alpha2"
 	"sigs.k8s.io/jobset/pkg/util/testing"
@@ -131,6 +132,87 @@ var _ = ginkgo.Describe("JobSet", func() {
 		})
 	})
 
+	ginkgo.When("job is unsuspended and suspend", func() {
+
+		ginkgo.It("should allow to resume a JobSet after PodTemplate was restored on suspend", func() {
+			ctx := context.Background()
+			js := shortSleepTestJobSet(ns).Obj()
+			jsKey := types.NamespacedName{Name: js.Name, Namespace: js.Namespace}
+
+			ginkgo.By("Create a suspended JobSet", func() {
+				js.Spec.Suspend = ptr.To(true)
+				js.Spec.TTLSecondsAfterFinished = ptr.To[int32](5)
+				gomega.Expect(k8sClient.Create(ctx, js)).Should(gomega.Succeed())
+			})
+
+			ginkgo.By("Unsuspend the JobSet setting nodeSelectors that prevent pods from being scheduled", func() {
+				gomega.Eventually(func() error {
+					gomega.Expect(k8sClient.Get(ctx, jsKey, js)).Should(gomega.Succeed())
+					js.Spec.Suspend = ptr.To(false)
+					podTemplate := &js.Spec.ReplicatedJobs[0].Template.Spec.Template
+					if podTemplate.Spec.NodeSelector == nil {
+						podTemplate.Spec.NodeSelector = make(map[string]string)
+					}
+					podTemplate.Spec.NodeSelector["kubernetes.io/hostname"] = "non-existing-node"
+					if podTemplate.Labels == nil {
+						podTemplate.Labels = make(map[string]string)
+					}
+					podTemplate.Labels["custom-label-key"] = "custom-label-value"
+					if podTemplate.Annotations == nil {
+						podTemplate.Annotations = make(map[string]string)
+					}
+					podTemplate.Annotations["custom-annotation-key"] = "custom-annotation-value"
+					return k8sClient.Update(ctx, js)
+				}, timeout, interval).Should(gomega.Succeed())
+			})
+
+			ginkgo.By("Await for all Jobs to be active", func() {
+				gomega.Eventually(func() int32 {
+					gomega.Expect(k8sClient.Get(ctx, jsKey, js)).Should(gomega.Succeed())
+					if js.Status.ReplicatedJobsStatus == nil {
+						return 0
+					}
+					return js.Status.ReplicatedJobsStatus[0].Active
+				}, timeout, interval).Should(gomega.Equal(js.Spec.ReplicatedJobs[0].Replicas))
+			})
+
+			ginkgo.By("Suspend the JobSet restoring the PodTemplate properties", func() {
+				gomega.Eventually(func() error {
+					gomega.Expect(k8sClient.Get(ctx, jsKey, js)).Should(gomega.Succeed())
+					js.Spec.Suspend = ptr.To(true)
+					podTemplate := &js.Spec.ReplicatedJobs[0].Template.Spec.Template
+					delete(podTemplate.Spec.NodeSelector, "kubernetes.io/hostname")
+					delete(podTemplate.Labels, "custom-label-key")
+					delete(podTemplate.Annotations, "custom-annotation-key")
+					podTemplate.Spec.SchedulingGates = nil
+					return k8sClient.Update(ctx, js)
+				}, timeout, interval).Should(gomega.Succeed())
+			})
+
+			ginkgo.By("Await for all Jobs to be suspended", func() {
+				gomega.Eventually(func() int32 {
+					gomega.Expect(k8sClient.Get(ctx, jsKey, js)).Should(gomega.Succeed())
+					if js.Status.ReplicatedJobsStatus == nil {
+						return 0
+					}
+					return js.Status.ReplicatedJobsStatus[0].Suspended
+				}, timeout, interval).Should(gomega.Equal(js.Spec.ReplicatedJobs[0].Replicas))
+			})
+
+			ginkgo.By("Unsuspending the JobSet again with PodTemplate allowing completion", func() {
+				gomega.Eventually(func() error {
+					gomega.Expect(k8sClient.Get(ctx, jsKey, js)).Should(gomega.Succeed())
+					js.Spec.Suspend = ptr.To(false)
+					return k8sClient.Update(ctx, js)
+				}, timeout, interval).Should(gomega.Succeed())
+			})
+
+			ginkgo.By("Await for the JobSet to complete successfully", func() {
+				util.JobSetCompleted(ctx, k8sClient, js, timeout)
+			})
+		})
+	})
+
 }) // end of Describe
 
 // getPingCommand returns ping command for 4 hostnames
@@ -246,3 +328,25 @@ func sleepTestJobSet(ns *corev1.Namespace) *testing.JobSetWrapper {
 			Replicas(int32(replicas)).
 			Obj())
 }
+
+func shortSleepTestJobSet(ns *corev1.Namespace) *testing.JobSetWrapper {
+	jsName := "js"
+	rjobName := "rjob"
+	replicas := 3
+	return testing.MakeJobSet(jsName, ns.Name).
+		ReplicatedJob(testing.MakeReplicatedJob(rjobName).
+			Job(testing.MakeJobTemplate("job", ns.Name).
+				PodSpec(corev1.PodSpec{
+					RestartPolicy: "Never",
+					Containers: []corev1.Container{
+						{
+							Name:    "short-sleep-test-container",
+							Image:   "bash:latest",
+							Command: []string{"bash", "-c"},
+							Args:    []string{"sleep 1"},
+						},
+					},
+				}).Obj()).
+			Replicas(int32(replicas)).
+			Obj())
+}