diff --git a/stan/math/rev/fun/csr_matrix_times_vector.hpp b/stan/math/rev/fun/csr_matrix_times_vector.hpp
index 4a0a93876e4..4665c7a4dbd 100644
--- a/stan/math/rev/fun/csr_matrix_times_vector.hpp
+++ b/stan/math/rev/fun/csr_matrix_times_vector.hpp
@@ -11,6 +11,119 @@
 namespace stan {
 namespace math {
 
+namespace internal {
+/**
+ * `vari` for csr_matrix_times_vector
+ * @note `csr_matrix_times_vector` uses the old inheritance
+ *  style to set up the reverse pass because of a linking
+ *  issue on windows when using flto.
+ *
+ * @tparam Result_ Either a type inheriting from `Eigen::DenseBase` with scalar
+ * type `var` or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+ * @tparam WMat_ Either a type inheriting from `Eigen::DenseBase` with scalar
+ * type `var` or `double`. Or a `var<T>` where `T` inherits from
+ * `Eigen::SparseBase`
+ * @tparam B_ Either a type inheriting from `Eigen::DenseBase` with scalar type
+ * `var` or `double`. Or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+ *
+ */
+template <typename Result_, typename WMat_, typename B_>
+struct csr_adjoint : public vari {
+  std::decay_t<Result_> res_;
+  std::decay_t<WMat_> w_mat_;
+  std::decay_t<B_> b_;
+
+  template <typename T1, typename T2, typename T3>
+  csr_adjoint(T1&& res, T2&& w_mat, T3&& b)
+      : vari(0.0),
+        res_(std::forward<T1>(res)),
+        w_mat_(std::forward<T2>(w_mat)),
+        b_(std::forward<T3>(b)) {}
+
+  void chain() { chain_internal(res_, w_mat_, b_); }
+
+  /**
+   * Overload for calculating adjoints of `w_mat` and `b`
+   * @tparam Result Either a type inheriting from `Eigen::DenseBase` with scalar
+   * type `var` or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+   * @tparam WMat Either a type inheriting from `Eigen::DenseBase` with scalar
+   * type `var`. Or a `var<T>` where `T` inherits from `Eigen::SparseBase`
+   * @tparam B Either a type inheriting from `Eigen::DenseBase` with scalar type
+   * `var`. Or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+   * @param res The vector result of the forward pass calculation
+   * @param w_mat A sparse matrix
+   * @param b A vector
+   */
+  template <typename Result, typename WMat, typename B,
+            require_rev_matrix_t<WMat>* = nullptr,
+            require_rev_matrix_t<B>* = nullptr>
+  inline void chain_internal(Result&& res, WMat&& w_mat, B&& b) {
+    w_mat.adj() += res.adj() * b.val().transpose();
+    b.adj() += w_mat.val().transpose() * res.adj();
+  }
+
+  /**
+   * Overload for calculating adjoints of `w_mat`
+   * @tparam Result Either a type inheriting from `Eigen::DenseBase` with scalar
+   * type `var` or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+   * @tparam WMat Either a type inheriting from `Eigen::DenseBase` with scalar
+   * type `var`. Or a `var<T>` where `T` inherits from `Eigen::SparseBase`
+   * @tparam B Either a type inheriting from `Eigen::DenseBase` with scalar type
+   * `double`
+   * @param res The vector result of the forward pass calculation
+   * @param w_mat A sparse matrix
+   * @param b A vector
+   */
+  template <typename Result, typename WMat, typename B,
+            require_rev_matrix_t<WMat>* = nullptr,
+            require_not_rev_matrix_t<B>* = nullptr>
+  inline void chain_internal(Result&& res, WMat&& w_mat, B&& b) {
+    w_mat.adj() += res.adj() * b.transpose();
+  }
+
+  /**
+   * Overload for calculating adjoints of `b`
+   * @tparam Result Either a type inheriting from `Eigen::DenseBase` with scalar
+   * type `var` or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+   * @tparam WMat Either a type inheriting from `Eigen::DenseBase` with scalar
+   * type `double`
+   * @tparam B Either a type inheriting from `Eigen::DenseBase` with scalar type
+   * `var` or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+   * @param res The vector result of the forward pass calculation
+   * @param w_mat A sparse matrix
+   * @param b A vector
+   */
+  template <typename Result, typename WMat, typename B,
+            require_not_rev_matrix_t<WMat>* = nullptr,
+            require_rev_matrix_t<B>* = nullptr>
+  inline void chain_internal(Result&& res, WMat&& w_mat, B&& b) {
+    b.adj() += w_mat.transpose() * res.adj();
+  }
+};
+
+/**
+ * Helper function to construct the csr_adjoint struct.
+ * @tparam Result_ Either a type inheriting from `Eigen::DenseBase` with scalar
+ * type `var` or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+ * @tparam WMat_ Either a type inheriting from `Eigen::DenseBase` with scalar
+ * type `var` or `double`. Or a `var<T>` where `T` inherits from
+ * `Eigen::SparseBase`
+ * @tparam B_ Either a type inheriting from `Eigen::DenseBase` with scalar type
+ * `var` or `double`. Or a `var<T>` where `T` inherits from `Eigen::DenseBase`
+ *
+ * @param res The vector result of the forward pass calculation
+ * @param w_mat A sparse matrix
+ * @param b A vector
+ */
+template <typename Result_, typename WMat_, typename B_>
+inline void make_csr_adjoint(Result_&& res, WMat_&& w_mat, B_&& b) {
+  new csr_adjoint<std::decay_t<Result_>, std::decay_t<WMat_>, std::decay_t<B_>>(
+      std::forward<Result_>(res), std::forward<WMat_>(w_mat),
+      std::forward<B_>(b));
+  return;
+}
+}  // namespace internal
+
 /**
  * \addtogroup csr_format
  * Return the multiplication of the sparse matrix (specified by
@@ -74,10 +187,7 @@ inline auto csr_matrix_times_vector(int m, int n, const T1& w,
     sparse_var_value_t w_mat_arena
         = to_soa_sparse_matrix<Eigen::RowMajor>(m, n, w, u_arena, v_arena);
     arena_t<return_t> res = w_mat_arena.val() * value_of(b_arena);
-    reverse_pass_callback([res, w_mat_arena, b_arena]() mutable {
-      w_mat_arena.adj() += res.adj() * b_arena.val().transpose();
-      b_arena.adj() += w_mat_arena.val().transpose() * res.adj();
-    });
+    stan::math::internal::make_csr_adjoint(res, w_mat_arena, b_arena);
     return return_t(res);
   } else if (!is_constant<T2>::value) {
     arena_t<promote_scalar_t<var, T2>> b_arena = b;
@@ -85,18 +195,14 @@ inline auto csr_matrix_times_vector(int m, int n, const T1& w,
     sparse_val_mat w_val_mat(m, n, w_val_arena.size(), u_arena.data(),
                              v_arena.data(), w_val_arena.data());
     arena_t<return_t> res = w_val_mat * value_of(b_arena);
-    reverse_pass_callback([w_val_mat, res, b_arena]() mutable {
-      b_arena.adj() += w_val_mat.transpose() * res.adj();
-    });
+    stan::math::internal::make_csr_adjoint(res, w_val_mat, b_arena);
     return return_t(res);
   } else {
     sparse_var_value_t w_mat_arena
         = to_soa_sparse_matrix<Eigen::RowMajor>(m, n, w, u_arena, v_arena);
     auto b_arena = to_arena(value_of(b));
     arena_t<return_t> res = w_mat_arena.val() * b_arena;
-    reverse_pass_callback([res, w_mat_arena, b_arena]() mutable {
-      w_mat_arena.adj() += res.adj() * b_arena.transpose();
-    });
+    stan::math::internal::make_csr_adjoint(res, w_mat_arena, b_arena);
     return return_t(res);
   }
 }