It is evangelistic. God’s Word is what converts sinners (Rom. 10:17; 1 Pet 1:23). Faithfully preaching God’s Word week after week exposes dead sinners to the only source of spiritual life: God’s Word. So expositional preaching is inherently evangelistic.
Preach the gospel in every sermon. Every text in the Bible, rightly understood, relates to the person and saving work of Jesus Christ (Luke 24:27, 44). No passage of Scripture can be rightly understood apart from Christ’s atoning death and resurrection. So every expositional sermon should also be an evangelistic sermon! The preacher should always find at least one way that the text leads to the gospel and take a moment during the sermon to clearly explain then gospel.
Directly address non-Christians. Consider what points in your sermon a non-Christians might misunderstand or reject out of hand and then address them personally at those points. A pastor can simply say, “If you’re here today and you haven’t repented of your sins and put your trust in Christ, I wonder what you think about what I just said…” Addressing non-Christians personally is a great way to show them that the Word of God is relevant to their lives, that they should engage with you because you are engaging with them, and that they are welcome in your church.