diff --git a/src/gui/opengl/qopenglextensions_p.h b/src/gui/opengl/qopenglextensions_p.h
index aa712f51a3..aa2f784d86 100644
--- a/src/gui/opengl/qopenglextensions_p.h
+++ b/src/gui/opengl/qopenglextensions_p.h
@@ -72,6 +72,9 @@ public:
     void (QOPENGLF_APIENTRYP CompressedTexImage3D)(GLenum target, GLint level, GLenum internalFormat, GLsizei width, GLsizei height, GLsizei depth, GLint border, GLsizei imageSize, const GLvoid *data);
     void (QOPENGLF_APIENTRYP CompressedTexSubImage3D)(GLenum target, GLint level, GLint xoffset, GLint yoffset, GLint zoffset, GLsizei width, GLsizei height, GLsizei depth, GLenum format, GLsizei imageSize, const GLvoid *data);
 
+    void (QOPENGLF_APIENTRYP TexStorage3D)(GLenum target, GLsizei levels, GLenum internalFormat, GLsizei width, GLsizei height, GLsizei depth);
+    void (QOPENGLF_APIENTRYP TexStorage2D)(GLenum target, GLsizei levels, GLenum internalFormat, GLsizei width, GLsizei height);
+
 private:
     QLibrary m_gl;
 };
diff --git a/src/gui/opengl/qopenglfunctions.cpp b/src/gui/opengl/qopenglfunctions.cpp
index aefea9a0e9..587995515d 100644
--- a/src/gui/opengl/qopenglfunctions.cpp
+++ b/src/gui/opengl/qopenglfunctions.cpp
@@ -3229,7 +3229,10 @@ QOpenGLES3Helper::QOpenGLES3Helper()
         CompressedTexImage3D = (void (QOPENGLF_APIENTRYP)(GLenum, GLint, GLenum, GLsizei, GLsizei, GLsizei, GLint, GLsizei, const GLvoid *)) m_gl.resolve("glCompressedTexImage3D");
         CompressedTexSubImage3D = (void (QOPENGLF_APIENTRYP)(GLenum, GLint, GLint, GLint, GLint, GLsizei, GLsizei, GLsizei, GLenum, GLsizei, const GLvoid *)) m_gl.resolve("glCompressedTexSubImage3D");
 
-        if (!MapBufferRange || !GenVertexArrays || !TexImage3D)
+        TexStorage3D = (void (QOPENGLF_APIENTRYP)(GLenum, GLsizei, GLenum, GLsizei, GLsizei, GLsizei)) m_gl.resolve("glTexStorage3D");
+        TexStorage2D = (void (QOPENGLF_APIENTRYP)(GLenum, GLsizei, GLenum, GLsizei, GLsizei)) m_gl.resolve("glTexStorage2D");
+
+        if (!MapBufferRange || !GenVertexArrays || !TexImage3D || !TexStorage3D)
             qFatal("OpenGL ES 3.0 entry points not found");
     } else {
         qFatal("Failed to load libGLESv2");
diff --git a/src/gui/opengl/qopengltexturehelper.cpp b/src/gui/opengl/qopengltexturehelper.cpp
index 3f55dfdba7..386c4af232 100644
--- a/src/gui/opengl/qopengltexturehelper.cpp
+++ b/src/gui/opengl/qopengltexturehelper.cpp
@@ -201,13 +201,16 @@ QOpenGLTextureHelper::QOpenGLTextureHelper(QOpenGLContext *context)
     TexImage2DMultisample = 0;
 
     // OpenGL 4.2
-#ifdef QT_OPENGL_ES_3
-    TexStorage3D = ::glTexStorage3D;
-    TexStorage2D = ::glTexStorage2D;
-#else
-    TexStorage3D = 0;
-    TexStorage2D = 0;
-#endif
+    QOpenGLContext *ctx = QOpenGLContext::currentContext();
+    if (ctx->format().majorVersion() >= 3) {
+        // OpenGL ES 3.0+ has immutable storage for 2D and 3D at least.
+        QOpenGLES3Helper *es3 = static_cast<QOpenGLExtensions *>(ctx->functions())->gles3Helper();
+        TexStorage3D = es3->TexStorage3D;
+        TexStorage2D = es3->TexStorage2D;
+    } else {
+        TexStorage3D = 0;
+        TexStorage2D = 0;
+    }
     TexStorage1D = 0;
 
     // OpenGL 4.3