diff --git a/sdk/storage/Azure.Storage.Blobs/src/BlobClient.cs b/sdk/storage/Azure.Storage.Blobs/src/BlobClient.cs
index 8df652fc58366..c91a776426f0e 100644
--- a/sdk/storage/Azure.Storage.Blobs/src/BlobClient.cs
+++ b/sdk/storage/Azure.Storage.Blobs/src/BlobClient.cs
@@ -1042,13 +1042,18 @@ public virtual Response<BlobContentInfo> Upload(
         public virtual Response<BlobContentInfo> Upload(
             BinaryData content,
             BlobUploadOptions options,
-            CancellationToken cancellationToken = default) =>
-            StagedUploadInternal(
-                content.ToStream(),
-                options,
-                async: false,
-                cancellationToken: cancellationToken)
-                .EnsureCompleted();
+            CancellationToken cancellationToken = default)
+        {
+            using (var stream = content.ToStream())
+            {
+                return StagedUploadInternal(
+                    stream,
+                    options,
+                    async: false,
+                    cancellationToken: cancellationToken)
+                    .EnsureCompleted();
+            }
+        }
 
         /// <summary>
         /// The <see cref="Upload(Stream, BlobHttpHeaders, Metadata, BlobRequestConditions, IProgress{long}, AccessTier?, StorageTransferOptions, CancellationToken)"/>
@@ -1360,13 +1365,18 @@ await StagedUploadInternal(
         public virtual async Task<Response<BlobContentInfo>> UploadAsync(
             BinaryData content,
             BlobUploadOptions options,
-            CancellationToken cancellationToken = default) =>
-            await StagedUploadInternal(
-                content.ToStream(),
-                options,
-                async: true,
-                cancellationToken: cancellationToken)
-            .ConfigureAwait(false);
+            CancellationToken cancellationToken = default)
+        {
+            using (var stream = content.ToStream())
+            {
+                return await StagedUploadInternal(
+                    stream,
+                    options,
+                    async: true,
+                    cancellationToken: cancellationToken)
+                .ConfigureAwait(false);
+            }
+        }
 
         /// <summary>
         /// The <see cref="UploadAsync(Stream, BlobHttpHeaders, Metadata, BlobRequestConditions, IProgress{long}, AccessTier?, StorageTransferOptions, CancellationToken)"/>
diff --git a/sdk/storage/Azure.Storage.Blobs/src/BlockBlobClient.cs b/sdk/storage/Azure.Storage.Blobs/src/BlockBlobClient.cs
index f5348303e57f0..f9269ce6cb893 100644
--- a/sdk/storage/Azure.Storage.Blobs/src/BlockBlobClient.cs
+++ b/sdk/storage/Azure.Storage.Blobs/src/BlockBlobClient.cs
@@ -3238,14 +3238,18 @@ await client.StageBlockInternal(
                             LeaseId = args.Conditions.LeaseId
                         };
                     }
-                    await client.StageBlockInternal(
-                            Shared.StorageExtensions.GenerateBlockId(offset),
-                            content.ToStream(),
-                            validationOptions,
-                            conditions,
-                            progressHandler,
-                            async,
-                            cancellationToken).ConfigureAwait(false);
+
+                    using (var stream = content.ToStream())
+                    {
+                        await client.StageBlockInternal(
+                                Shared.StorageExtensions.GenerateBlockId(offset),
+                                stream,
+                                validationOptions,
+                                conditions,
+                                progressHandler,
+                                async,
+                                cancellationToken).ConfigureAwait(false);
+                    }
                 },
                 CommitPartitionedUpload = async (partitions, args, async, cancellationToken)
                     => await client.CommitBlockListInternal(