Allaah, all Glory and Praise be to Him, has said:
"Verily, your Lord has said: 'Call upon Me, and I will answer you!' Indeed, those who disdain My worship will enter Hell, humiliated." (Soorah Ghaafir, 40:60)
In this verse, Allaah سبحانه و تعالى has commanded us to ask Him and petition Him, and counted those who do not ask Him among those who are too arrogant to worship Allaah سبحانه و تعالى. From this, it is understood that du'aa' is among the acts of worship, and this meaning was explicitly stated by the Prophet. Sayyiduna Nu'maan Ibn Basheer رضي الله عنه reports that the Prophet صلى الله عليه وسلم said: "Du'aa' is worship." He then recited the verse:
"Verily, your Lord has said: 'Call upon Me, and I will answer you!' Indeed, those who disdain My worship will enter Hell, humiliated." (Soorah Ghaafir, 40:60) 
Therefore, du'aa' is a type of worship; rather, it is amongst the greatest acts of worship, and one of the best ways to bring a worshipper closer to Allaah, all Glory and Praise be to Him. In this verse, Allaah سبحانه و تعالى has equated du'aa' with worship, for He commanded His servants to make du'aa' to Him, and then stated that whoever is too arrogant to worship Him will enter the Fire of Hell. So from this it is understood that the worship referred to in this verse actually means du'aa'.
In another verse, Allaah سبحانه و تعالى calls du'aa' the 'deen' or the entire religion, for He says:
"He is al-Hayy (the Ever-Living), none has the right to be worshipped but He. So make du'aa' to Him, to Him is the deen. [All] praise is [due] to Allah , Lord of the worlds." (Soorah Ghaafir, 40:65)
And there is no other act that has been equated or paralleled with the entire deen, or connected to the entire concept of worship ('ibaadah).
One of the benefits that are obtained by realising that du'aa' is a form of worship is that the manner and procedure of du'aa' must only be taken from the Qur'aan and Sunnah. Just as a person cannot use his mind or whims to decide how to pray or fast, so too must he restrain to the texts of the Qur'aan and Sunnah when it comes to the manner and etiquettes of du'aa'. 
 This hadeeth is authentic, and is reported by Ahmad and the four Sunan, and others, from Nu'maan Ibn Basheer رضي الله عنه, as reported in Saheeh al-Jaami' #3407.
 Dua: The Weapon of the Believer