The answer to the above question is very straightforward...
1 Timothy 2:1-7 is a great passage to help us understand the importance of evangelistic prayer. Why not read the 1st installment of a multi-part devotional below to learn more about the need for evangelistic prayer.
"First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all people, for kings and all who are in high positions, that we may lead a peaceful and quiet life, godly and dignified in every way. This is good, and it is pleasing in the sight of God our Savior, who desires all people to be saved and to come to the knowledge of the truth. For there is one God, and there is one mediator between God and men, the man Christ Jesus, who gave himself as a ransom for all, which is the testimony given at the proper time. For this I was appointed a preacher and an apostle (I am telling the truth, I am not lying), a teacher of the Gentiles in faith and truth." (1 Timothy 2:1-7, ESV)
In the above text we read Paul now a converted man and an Apostle of the Lord Jesus, spurring Christians on to what had no doubt become a central part of his own ministry – the great work of evangelistic prayer.
First, he tells us:
What it Includes...
First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made…
(1 Timothy 2:1 ESV)
The primary mission and aim of the church concerns the prayerful and open communication of the gospel to men and women, boys and girls. We exist, if you like, as the public relations arm of the Kingdom of Heaven - and that is why Paul says, this is “first” of all (v.1a). Of all the things the church is commissioned to do communicating the good news of Jesus Christ is "first." Because this work is so important we must commit it to prayer - four types of which are referenced by Paul in v.1 and run as follows:
This word carries with it the idea of “being without something.” To put it another way, evangelistic prayer comes from a sense of need. We call upon God to supply what is lacking and what is lacking – for many in our world, is saving faith.
This reality should spur us on in our supplications... the understanding that my children, my neighbor, my spouse, and my friends are all never-dying souls who will live somewhere in eternity forever, should cause us to to engage in supplications.
This is a general word for prayer in the bible and it carries with it the idea of worship with reverence. Paul is telling us that part of worshiping God with reverence involves calling on Him to save lost people.
This is the idea of getting alongside someone. It is a prayer in which the one praying identifies with those he’s praying for. It is appealing to God based upon the fact that you can Identify with people's need for the gospel. And why can you identify with their need for the gospel? Because you need it yourself.
This is gratitude to God for the fact that there is a gospel is the first place. Could you imagine if there weren't? But there is! Right here in a world of bad-news there is a God-given message of good-news! Moreover, out of all of the people on planet earth, we - the Church - have been given the privilege and responsibility to bring this good news to bear upon ourselves and to take it to others. Because of this our prayers should be filled with thankfulness and total reliance upon the reality that the gospel is the means through which God answers our evangelistic "supplications, prayers, intercessions, and thanksgivings."
(1 Timothy 2:1 ESV)