diff --git a/modules/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java b/modules/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java
index f2bba1a79a57d..80bd788da9a9f 100644
--- a/modules/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java
+++ b/modules/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java
@@ -10,10 +10,12 @@
 
 import fixture.azure.AzureHttpFixture;
 
+import com.azure.core.exception.HttpResponseException;
 import com.azure.storage.blob.BlobContainerClient;
 import com.azure.storage.blob.BlobServiceClient;
 import com.azure.storage.blob.models.BlobStorageException;
 
+import org.elasticsearch.ExceptionsHelper;
 import org.elasticsearch.action.ActionRunnable;
 import org.elasticsearch.action.support.PlainActionFuture;
 import org.elasticsearch.action.support.master.AcknowledgedResponse;
@@ -188,8 +190,8 @@ public void testMultiBlockUpload() throws Exception {
 
     public void testReadFromPositionLargerThanBlobLength() {
         testReadFromPositionLargerThanBlobLength(
-            e -> asInstanceOf(BlobStorageException.class, e.getCause()).getStatusCode() == RestStatus.REQUESTED_RANGE_NOT_SATISFIED
-                .getStatus()
+            e -> asInstanceOf(BlobStorageException.class, ExceptionsHelper.unwrap(e, HttpResponseException.class))
+                .getStatusCode() == RestStatus.REQUESTED_RANGE_NOT_SATISFIED.getStatus()
         );
     }
 }
diff --git a/modules/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobContainer.java b/modules/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobContainer.java
index d271c8d1e99a1..eb643b3c1460d 100644
--- a/modules/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobContainer.java
+++ b/modules/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobContainer.java
@@ -8,11 +8,11 @@
 
 package org.elasticsearch.repositories.azure;
 
-import com.azure.storage.blob.models.BlobStorageException;
+import com.azure.core.exception.HttpResponseException;
 
 import org.apache.logging.log4j.LogManager;
 import org.apache.logging.log4j.Logger;
-import org.apache.logging.log4j.core.util.Throwables;
+import org.elasticsearch.ExceptionsHelper;
 import org.elasticsearch.action.ActionListener;
 import org.elasticsearch.common.Strings;
 import org.elasticsearch.common.blobstore.BlobContainer;
@@ -69,13 +69,13 @@ private InputStream openInputStream(OperationPurpose purpose, String blobName, l
         try {
             return blobStore.getInputStream(blobKey, position, length);
         } catch (Exception e) {
-            Throwable rootCause = Throwables.getRootCause(e);
-            if (rootCause instanceof BlobStorageException blobStorageException) {
-                if (blobStorageException.getStatusCode() == RestStatus.NOT_FOUND.getStatus()) {
+            if (ExceptionsHelper.unwrap(e, HttpResponseException.class) instanceof HttpResponseException httpResponseException) {
+                final var httpStatusCode = httpResponseException.getResponse().getStatusCode();
+                if (httpStatusCode == RestStatus.NOT_FOUND.getStatus()) {
                     throw new NoSuchFileException("Blob [" + blobKey + "] not found");
                 }
-                if (blobStorageException.getStatusCode() == RestStatus.REQUESTED_RANGE_NOT_SATISFIED.getStatus()) {
-                    throw new RequestedRangeNotSatisfiedException(blobKey, position, length == null ? -1 : length, blobStorageException);
+                if (httpStatusCode == RestStatus.REQUESTED_RANGE_NOT_SATISFIED.getStatus()) {
+                    throw new RequestedRangeNotSatisfiedException(blobKey, position, length == null ? -1 : length, e);
                 }
             }
             throw new IOException("Unable to get input stream for blob [" + blobKey + "]", e);
diff --git a/muted-tests.yml b/muted-tests.yml
index 96fc68cdc3b8a..26be6e9389368 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -97,9 +97,6 @@ tests:
 - class: org.elasticsearch.xpack.security.authc.oidc.OpenIdConnectAuthIT
   method: testAuthenticateWithImplicitFlow
   issue: https://github.com/elastic/elasticsearch/issues/111191
-- class: org.elasticsearch.repositories.azure.AzureBlobContainerRetriesTests
-  method: testReadNonexistentBlobThrowsNoSuchFileException
-  issue: https://github.com/elastic/elasticsearch/issues/111233
 - class: org.elasticsearch.action.admin.indices.create.SplitIndexIT
   method: testSplitIndexPrimaryTerm
   issue: https://github.com/elastic/elasticsearch/issues/111282