The problem

The Zorbo's attack does the following on a hit:

Hit: 8 (2d6 + 1) slashing damage, and if the target is a creature wearing armor, carrying a shield, or in possession of a magic item that improves its AC, it must make a DC11 Dexterity saving throw. On a failed save...

There are thus two primary consequences of being hit by a Zorbo; taking damage, and making a save. If the damage reduces the target to zero hp, there is the further, secondary consequence of falling unconscious, which includes going prone and applying the unconscious condition. Thus a single hit can generate at least four consequences, and some of these consequences can be affected by the order in which they are applied - as you point out, the Dex save is automatically failed if the unconscious condition has been applied before the save is made. Order matters.

What the rules say - and don't say

The rules on Making an Attack say:

Whether you're striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.

1. Choose a target...
2. Determine modifiers...
3. Resolve the attack. You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage.

Step three, resolving the attack, contains all of the guidance we are given in how to apply simultaneous consequences of a hit - that is, practically none. "Some attacks cause special effects in addition to...damage" is all we have to work with. In particular, the 5e rules are very much unlike a game like M:tG, where simultaneous effects have a precisely defined priority that determines their order of resolution.

Like many aspects of 5e, it then becomes the job of the DM to decide the order in which to apply the multiple effects of a hit.

Solars and Slaying Longbows

The Solar has an attack called Slaying Longbow which does:

Hit: 15 (2d8 + 6) piercing damage plus 27 (6d8) radiant damage. If the target is a creature that has 100 hit points or fewer, it must succeed on a DC 15 Constitution saving throw or die.

Since the damage from the hit itself could reduce the target to fewer than 100hp and thus force the save, Jeremy Crawford was once asked the order in which to apply the consequences of the hit. His response was:

Slaying Longbow sequence:

1. Hit
2. Deal damage (apply any resistance)
3. Make saving throw if the target has hit points ≤ 100

At first blush, this seems pretty similar to the Zorbo situation, so if you want to take this as RAI you can; first apply the damage, and the consequences of the damage including unconsciousness, and then the save. However, it is important to be aware that Crawford's tweets are not official. Further, even if you accept this it is unclear whether it is meant as a specific statement about how the slaying longbow works or a general statement about the order of simultaneous events, or even something in between like 'apply them in the order required to make the save happen, but not an automatic fail.'

An optional rule

Given the lack of an official rule in the ordering of resolution of simultaneously-triggered events, it is unsurprising that there is an optional rule, as presented in XGtE:

If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen.

In general, this is a pretty good practice. It can resolve any number of simultaneously-triggered effects. It gives more agency to players on their own turns, while being fair to everyone involved. It can usually align with supporting the narrative. In your case of the Zorbo, if the Zorbo's attack happened on the Zorbo's turn, the monster would clearly want the save to automatically fail. In that moment the monster has the initiative, and overwhelms the character before the character can respond. On the other hand, if this happened on the player's turn, where the Zorbo's attack was a reaction, it makes narrative sense that the character with the initiative darted away from the Zorbo, was wounded, but maintained consciousness just long enough to attempt the save before succumbing to their wounds and falling unconscious.

Where I would not use Xanathar's

In certain situations, a strict application of the optional rule in XGtE results in diminished verisimilitude. Consider the poisoned crossbow bolt of a drow, which has:

Hit: (1d6 + 2) piercing damage. The target must succeed on a DC 13 constitution saving throw or be poisoned for 1 hour. If the saving throw fails by 5 or more, the target is also unconscious while poisoned in this way. The target wakes up if it takes damage or if another creature takes an action to shake it awake.

Suppose a character is hit by a bolt on the character's own turn (such as when the drow had a readied action to fire upon a certain trigger). In this case, a player allowed to use the XGtE optional rule and order events as they chose could declare that they wanted to make the save first, and then, if they had been poisoned into unconsciousness, apply the damage in order to wake themselves up from the same hit that knocked them out. Clearly this goes against any reasonable application of the narrative, even if the character has initiative at that point. Thus, I would say that while the XGtE rule is generally good, DM's should feel free to override it when it conflicts with narrative verisimilitude. Fortunately in your case of the Zorbo, that doesn't appear to be an issue.