There are numerous places where Allah (s.w.t.) has referred to Hazrat Abutalib (as) in the Holy Quran.
Proof1
Surae Aale Imran Verse No. 33
إِنَّ اللّهَ اصْطَفَى آدَمَ وَنُوحًا وَآلَ إِبْرَاهِيمَ وَآلَ عِمْرَانَ عَلَى الْعَالَمِينَ
Allah did choose Adam and Noah, the family of Abraham, and the family of 'Imran above all people,-
Hazrat Abu Talib (as) was born in the year 540 A.H. in Mecca. Most of the scholars are of the opinion that your name was Imran and Abdutalib was your agnomen which was because of your son Talib. Allah (s.w.t.) had selected him for his important tasks which is evident from the above given verse of the Holy Quran.
Allah (s.w.t.) tells in the above verses that he chose the family Of Hazrat Abu Talib (as) above all people as he chose Adam (as), Nooh (as), and the family of Ibrahim (as),thus keeping them at par with each other.
As was the lofty position of Ibrahim (as) in front of Allah (s.w.t.) so was the position of Hazrat Abutalib (as).
Why would Allah (s.w.t.) choose the family of an unbeliever?, who does not believe in him, and allot him a lofty position as he allotted to his Prophets.
A point to be clarified over here is that in all there were three Imrans in history. The Father of Hazrat Musa (as), the father of Janabe Maryam (s.a) and the father of Hazrat Ali (as).
The Imran refered to over here could be non other than the father of Hazrat Ali (as) because the progeny of the other two Imrans were discontinued and its only the progeny of Hazrat Abutalib (as) that continues up till today.
Proof2
Sura e Balad Verse N. 1,2,3
لَا أُقْسِمُ بِهَذَا الْبَلَدِ وَأَنتَ حِلٌّ بِهَذَا الْبَلَدِ وَوَالِدٍ وَمَا وَلَدَ
Nay, I swear by this city, And thou art an indweller of this city,And the begetter and that which he beget,
I the above three verses of Sura e Balad Allah (s.w.t) swears by the city of Mecca and By the Holy Prophet and by the Begetter and which he beget.
Now the begetter and which he beget referred in this aayat are non other than Hazrat Abutalib (as) and his off springs. If no, then can then entire Islamic world find out One father and One son at that time who are worthy of Allah (s.w.t.)’s swear.
Hazrat Abutalib (as) and Hazrat Ali (as) helped the Holy Prophet (s.a.w.w) throughout their lives and helped to spread his mission.
Its against the standard of the High and the Majestic that he swears by something irrelevant. Thus the High and Majestic swearing by Hazrat Abu Talib (as) in fact shows his high and lofty position in the eyes of Allah (s.w.t.).
Allah (s.w.t.) swears not only by Hazrat Abu Talib (as) but also his off springs, this clearly shows that all the off springs of Hazrat Abu Talib (as) were devoted, religious, pious and virtuous people.
Any question on any of the off springs of Hazrat Abu Talib (as), including Hazrat Aqeel (as), in fact questions these words of Allah (s.w.t.).
Would Allah(s.w.t.) swear by an unbeliever..??
Proof3
Surae Zoha Verse No 6.
أَلَمْ يَجِدْكَ يَتِيمًا فَآوَى
Has He not found thee an orphan, and given thee shelter?
In the above Verse Allah (s.w.t.) calls the protection and care provided by Hazrat Abu Talib (as) as his care and His protection. Allah (s.w.t.) refers to the lap of Hazrat Abu Talib (as) as his own Lap.
This verse infact is a praise, euology and acknowledgement of Hazrat Abu Talib (as) lifelong service and selfless efforts.
Now, would Allah (s.w.t.) call the actions of an unbeliever as his own actions ...??
Proof4
Surae Ma'ida Verse No. 15
قَدْ جَاءكُم مِّنَ اللّهِ نُورٌ وَكِتَابٌ مُّبِينٌ
Now there has come unto you from God a light, and a clear divine writ,(5:15)
Allah (s.w.t) has reveled the Holy Quran as well as the Light of the Holy Prophet (s.a.w.w.) which are at par with each other. Infact according to the Ahadees of Aaima (as) the Light of Ahlulbait (as) is better then the Holy Quran because, the Holy Quran is Quran e Samit (silent) while the Holy Ahlulbait (as) are Quran e Natik (speaking).
Quran is Kalamullah, while Holy Ahlulbait (as) are Wajhullah, Ainullah, Jambhullah, Yadullah, Lisanullah, etc.
As the Holy Quran is never placed on a najis ‘rahal’ (stand), similarly this pure and pious noor could never be placed in najis and impure backs and wombs.
Proof5
Surae Aale Imran Verse No. 164
Let us pay attention to this verse of the Holy Quran in which Allah (s.w.t.) says:
لَقَدْ مَنَّ اللّهُ عَلَى الْمُؤمِنِينَ إِذْ بَعَثَ فِيهِمْ رَسُولاً مِّنْ أَنفُسِهِمْ يَتْلُو عَلَيْهِمْ آيَاتِهِ وَيُزَكِّيهِمْ وَيُعَلِّمُهُمُ الْكِتَابَ وَالْحِكْمَةَ وَإِن كَانُواْ مِن قَبْلُ لَفِي ضَلالٍ مُّبِينٍ
"Indeed, God bestowed a favour upon the believers when he raised up in their midst an apostle from among themselves, to convey His messages unto them, and to cause them to grow in purity, and to impart unto them the divine writ as well as wisdom....."
Now, in the above verse Allah (s.w.t.) says that he raised in the midst of beleivers an apostel which means that there were beleivers present at the time when the Holy Prophet (s.a.w.w.) declared his prophethood.
The word used for believers in the above verse is 'momeneena' which in Arabic stands for a minimum of three believers. Thus when the Holy Prophet (s.a.w.w.) declared his prophethood then there were atleast a minimum of three beleivers present.
Scholars are of the view that they were none but Hazrat Abutalib (as), Janabe Khadija (s.a.) and Hazrat Ali (as).
Would now people speak against the one whom Allah (s.w.t.) calls a believer.
Proof6
Surae Dahar Verse No 24
فَاصْبِرْ لِحُكْمِ رَبِّكَ وَلَا تُطِعْ مِنْهُمْ آثِمًا أَوْ كَفُورًا
Therefore be patient with constancy to the command of your Lord, and obey neither a sinner nor a disbeliever among them.
Allah (s.w.t.) tells the Holy Prophet (s.a.w.w.) not to follow the advice of a sinner or a disbeliever. Now it is a well known fact that the Holy Prophet (s.a.w.w.) spent 3 years of his life in Shib e Abutalib (as) only and only on the advice of his Uncle.
The Holy Prophet (s.a.w.w.) would never go against the orders of the Almighty (s.a.w.w.).
The illegitimate dispute about the faith of Hazrat Abutalib (as) whereas Allah (s.w.t.) tells that Hazrat Abutalib (as) was not only a believer but also free from all sins.
Not only was Hazrat Abutalib (as) a true believer but he was also a 'Masoom'.