Tawassul (beseeching Allah in the name of or by) the blessing of the Qur’an is permissible and not considered Shirk (associating others with Allah in His Divinity or worship).
Tawassul by the blessing of creatures, such as the Prophet (peace be upon him), is a condemned Bid‘ah (innovation in religion), because Tawassul is among the acts of worship that is Tawqifiy (bound by a religious text and not amenable to personal opinion). Nothing has been authentically reported in the sanctified Shari‘ah that permits this for creatures, in the name of their right, their honor, or their blessing. (Part No. 1; Page No. 521) It is authentically reported that the Messenger of Allah (peace be upon him) stated:
“Whoever does an action which is not in accordance with this matter of ours (Islam), will have it rejected.”
May Allah grant us success. Peace and blessings be upon our Prophet Muhammad, his family and Companions!