Many get all hung up when you use those two words together. It has become more appreciated due to a book several years ago by that very name. As worshippers we have a passion for God's glory. It is an awesome experience when all of God's people worship Him with heart, soul, mind, and strength. Some think we have to "dumb" that down to also have evangelism in our worship. However, scripture indicates that it is when the lost see and hear God's people worshipping Him that they are moved toward Him in the power of God's Spirit.
Apart from God our friends, neighbors and family members are lost. We should be motivated to let them see the Lord and Savior through our worship. But, you say, how does evangelism mix with worship. Well, our ultimate goal is to make them worshippers of Him. So, our motivation to love them and worship before them is part of that great commandant to love Him with all that we are, and others as ourselves.
Love for others, however, should not really be the primary driver for evangelism. Rather, our passion for God's glory should be the basic incentive that drives us to share the gospel with unbelievers. We should want all peoples to be able to hear and respond to His good news because as Psalm 48:1 says, "God is great and greatly to be praised."
As we grow in our faith and in our worship we should become more and more motivated by a zeal for God's glory in wanting to see others find out how wonderful and awesome God is. We grow in our desire for them to experience His love, not just so they can be healed and transformed but that they might give glory and honor to God with their whole lives, yes, so that they might worship Him!
May we worship Him with our whole heart seeking to add new worshippers to the community of faith! May we cover the earth with His glory "making His praise known to all". mjm