OHN 3:16 is commonly referred to as "the gospel in a nutshell." And, in Ephesians 2:8-10 we can read (in just a few verses) a marvelous summation of the gospel and its aftereffects. But here in Titus 3 we have what amounts to almost an entire chapter devoted to a clear description of the gospel of God's grace, and all that follows. Let's call this the gospel train.
Now, a train has a proper order to it. It would be strange indeed if one were to see a boxcar or two rolling down a railroad track all by themselves. Or, if there were never any cars, only. That would not make sense. But, if you see an engine pulling some cars (and in olden days, at last the caboose comes by), well that is what you would expect. That makes sense. Even so, in God's plan of redemption there is a proper order. This order is seen in this chapter.
At one time, we were all foolish sinners (vs. 3). The love of the Savior appears on our sinful scene though (vs. 4), and God regenerates the sinner, saving us from our sin & sealing us with His Spirit (vs. 5-6). As justified saints, we are the permanent possessors of the very life of God Himself (Titus 2:7). As God's children, we are obliged then to honor Him continually with our deeds (Titus 3:1, 8 & 14). The plan functions that way. That's the way it was designed to look.
Now, good works cannot precede salvation (Isaiah 64:6). Then again, salvation doesn't travel the tracks of God's grace alone (Revelation 14:13). While our good works most certainly do not contribute to our redemption, they do demonstrate it.