Does the Prophet's saying, peace and blessings be upon him, "I have left among you two matters," contradict the noble verse, "This day I have perfected for you your religion"?

There is no contradiction between religious texts because they are all revelations from Allah. Rather, contradictions may arise in the minds of some people. Interpreters have differed on the meaning of Allah's statement: (This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion) Al-Ma'idah/3, holding two views:

The first view: That what is meant is the perfection of religious laws concerning commands, prohibitions, and lawful and unlawful matters, as the religion became complete with its obligations, pillars, lawful and unlawful aspects after the revelation of this verse.

The second view: That what is meant by the perfection of religion is its triumph over its enemies, as people entered the religion of Allah in droves, and no polytheist performed Hajj with the Messenger of Allah, peace be upon him.

The correct understanding is that there is no impediment to applying the verse to both meanings simultaneously.

There is no contradiction between this verse and the saying of the Messenger of Allah, peace be upon him: "I have left among you that which, if you hold fast to it, you will never go astray after me: the Book of Allah." Narrated by Muslim (1218). And in a narration by Al-Hakim: "the Book of Allah and my Sunnah," authenticated by Al-Albani in "Sahih Al-Jami'" (2937).

If the meaning of the verse is the triumph of the religion, then the Hadith discusses another topic, which is adherence to the Book and the Sunnah.

And if the meaning of the verse is the completion of religious laws, then the Hadith confirms this and does not contradict it, because religious laws are received only from the Book and the Sunnah. The Book is the Qur'an, and wisdom is the Sunnah, and the religion is built upon these two foundations.

So the religion is complete, and the Messenger of Allah, peace be upon him, conveyed from Allah His commands, prohibitions, and lawful and unlawful matters.