add_action( 'validate_password_reset', 'rsm_redirect_after_rest', 10, 2 );
function rsm_redirect_after_rest($errors, $user) {
    if ( ( ! $errors->get_error_code() ) && isset( $_POST['pass1'] ) && !empty( $_POST['pass1'] ) ) {
        reset_password( $user, $_POST['pass1'] );
        setcookie( $rp_cookie, ' ', time() - YEAR_IN_SECONDS, $rp_path, COOKIE_DOMAIN, is_ssl(), true );
        wp_set_current_user( $user->ID );
        wp_set_auth_cookie( $user->ID );
        do_action( 'wp_login', $user->user_login );//`[Codex Ref.][1]
        wp_redirect( home_url() );
        exit;
    }
}