The New Revised Standard Version for Zechariah 9:9 says, "Rejoice greatly, O daughter Zion! Shout aloud, O daughter Jerusalem! Lo, your king comes to you; triumphant and victorious is he, humble and riding on a donkey, on a colt, the foal of a donkey."
How was the new king of Israel triumphant and victorious? Was Jesus triumphant and victorious when he entered Jerusalem on a donkey?
In my opinion, "triumphant" and "victorious" are not the best ways to translate tzadiq and nosha, respectively. Tzadiq most often means "righteous," and nosha is a niphal of yasha, which means "save." Niphal is often a passive form, so nosha may mean "saved." So one can say that the king who enters Jerusalem in Zechariah 9:9 is righteous and saved.
The king is righteous, in contrast to many of the previous kings of Israel and Judah, who led their nation to disaster. His righteousness makes him a lover of peace, which is why he will command peace to the nations (Zechariah 9:10). So this is not a king who will lead his people to divine punishment, nor will he allow imperialistic powers to bully Israel unjustly. He is a righteous king.
How is the king "saved"? He may be "saved" in the sense that he is delivered from battle. Perhaps he participated in God's wrath on the nearby nations in Zechariah 9:1-8 (e.g., Syria, Tyre, and Philistia), and he returns to Israel as a survivor of those many battles. The nations were strong, and the battles were many, so there was a good chance that the king could die, but he didn't.
Can this apply to Jesus? Maybe the interpretation that I just laid out cannot, for Jesus did not fight Syria, Tyre, and Philistia. Is there another interpretation that can work? Well, according to W. Sibley Towner in my HarperCollins Study Bible, "Commentators point out that the conquest of the eastern Mediterranean by Alexander the Great in 332 B.C.E. followed a similar course" to that of the divine warrior in Zechariah 9:1-8. So perhaps Zechariah 9:1-8 was fulfilled by Alexander the Great. Years later, the king of Israel, Jesus, would come to Jerusalem seated on a donkey. And, years after that, he would return to command peace to the nations.
Maybe Zechariah 9 does not have to be fulfilled all at once. Perhaps Zechariah (or, more precisely, Second Zechariah, the scholarly term for Zechariah 9-14) was telling the post-exilic community God's overall plan for his people, which would reach fulfillment over several years. "But why would they care about what happens centuries down the road?" one may ask. Well, we often hear that Israelites in those days had a communal mindset rather than an individualistic one. God could punish sin down to the third and fourth generation, after all. So perhaps the Israelites of Second Zechariah's time would be interested in what happened to their descendants.
So how was Jesus "saved"? For this question, I cannot really come up with an interpretation that is faithful both to the context of Zechariah 9:9 and also the life of Jesus. But I can think of ways in which Jesus experienced deliverance before he entered Jerusalem on a donkey. He had survived Herod's massacre of infants (Matthew 2) and the attempt of the Pharisees to kill him (Luke 4:29-30). The Jewish leaders had wanted to arrest Jesus during his ministry, but they couldn't because his hour had not yet come (John 7:30). Jesus had also done his share of battling the forces of darkness, for he bound and plundered Satan (Matthew 12:29). God had preserved Jesus' life through many conflicts and battles. In a manner of speaking, Jesus was "saved" by the time he entered Jerusalem on a donkey.
Of course, Zechariah 9 doesn't say anything about Jesus' close calls, but perhaps we can juxtapose Zechariah 9 with the life of Christ to say this: Whatever evil may throw at God's anointed king, God will deliver him so that he will accomplish God's salvific purpose. Zechariah 9 is about God overthrowing evil and setting up his kingdom of peace. Whenever God tries to destroy evil, evil will fight back. But God's anointed one, Jesus, would survive the battle.