What each method actually controls
A zero-based budget assigns every dollar of income to a category before the month starts, so income minus all assigned categories equals zero -- nothing left unassigned, nothing spent without a plan for it. It doesn't, by itself, say anything about debt order; it just insists every dollar has a named job. The debt snowball is a payoff order: list every debt smallest balance to largest, pay the minimum on all of them, and send every extra dollar available for debt at the smallest one until it's gone, then roll that whole payment -- minimum plus extra -- onto the next smallest. It doesn't say anything about how the rest of your budget should be organized. The two methods solve different problems, which is exactly why combining them takes a small amount of deliberate setup rather than happening automatically.
Where the two methods meet: one line, not many
The cleanest way to combine them is a single zero-based budget category called something like "Debt Snowball Payment," sized to the minimum-plus-extra total the snowball method says to pay this month. Everything about which specific debt that money goes to, and in what order, is the snowball's job, not the budget's -- the zero-based budget only needs to know the total dollar amount leaving that category, not track five separate minimum-payment line items plus a moving extra-payment amount. Fewer categories to reconcile at month end, less to get wrong.
What happens when a debt gets paid off mid-cycle
This is the part most explanations of either method skip. Say a snowball target gets its final payment in the middle of a month -- the debt hits zero and closes. The dollar amount that used to be that debt's minimum payment doesn't disappear from the budget and it doesn't become "extra" money to spend elsewhere: in a debt snowball, it immediately becomes part of next month's payment toward the next-smallest remaining debt. In zero-based-budget terms, this means the "Debt Snowball Payment" category's total dollar amount usually stays the same size (or keeps growing, if extra income appears) even as which specific debts it's aimed at changes underneath it -- the category doesn't shrink just because one debt inside it finished. If it does look like it should shrink (say the paid-off debt's minimum was unusually large relative to your total extra payment amount), that's worth double-checking against your own debt list rather than assuming, since it's the one case where the category total genuinely can change.
A worked example
Say three debts remain: a $400 balance at a $25 minimum, a $2,000 balance at a $60 minimum, and a $9,000 balance at a $150 minimum -- and the budget sends $300 total to debt each month (all three minimums plus $65 extra). The $400 debt clears in a couple of months. The next month's "Debt Snowball Payment" category is still $300 total -- but now it's $60 (second debt's minimum) plus $150 (third debt's minimum) plus $90 extra (the old $65 extra plus the $25 that used to be the paid-off debt's minimum), aimed at the $2,000 balance. The zero-based total didn't change; only the internal split did. These numbers are an illustration of the mechanic, not a recommendation for your own amounts -- your own minimums, balances, and extra-payment capacity will be different.
Handling a windfall without breaking the zero
A tax refund, bonus, or other one-time windfall is exactly the kind of income a strict zero-based budget has to plan for on purpose, because it arrives outside the normal monthly rhythm. The budget still needs to reach zero the moment that money is assigned -- it just means deciding, as soon as the windfall arrives (not after some of it has already been spent informally), how much goes to the debt snowball category versus other categories: an emergency fund top-off, a sinking fund that's behind schedule, or a discretionary category if that's the priority right now. There's no universally "correct" split -- that depends on your own financial priorities -- but deciding it deliberately, in one sitting, and assigning the whole amount to named categories is what keeps a windfall month zero-based instead of becoming an unplanned-spending month by default.
What to do when an irregular expense breaks the plan mid-month
A car repair or a medical bill that lands mid-month, after the debt snowball payment is already planned, forces a real choice: pull the money from somewhere else in the budget first, or reduce that month's snowball payment down to the minimums-only amount and resume the extra payment next month. Neither choice is a failure of the method. A zero-based budget that gets re-balanced mid-month when something unplanned happens is the budget working as intended; a zero-based budget that pretends the irregular expense didn't happen and goes negative somewhere else is the one actually breaking down. If this kind of irregular expense keeps recurring, it's often a sign a small sinking fund for that category (car repairs, medical costs) would absorb it more gracefully than the debt snowball payment having to flex every time.
Keeping minimums current as the debt list shrinks
Every time a debt closes, it's worth re-confirming the new smallest remaining balance and its actual current minimum payment directly with the lender or servicer, rather than assuming the number from a list made months earlier is still accurate -- minimum payments on revolving balances in particular can shift as the balance itself changes. A stale minimum-payment figure is the most common way a "Debt Snowball Payment" category quietly stops adding up correctly over time.
The bookkeeping problem this leaves you with
Once the method itself is clear, what's left is tracking: which debt is currently the target, what this month's total snowball payment is, and confirming the zero-based budget's other categories still add up to the rest of income. That's a bookkeeping problem a paper or spreadsheet system can carry for you once the decisions above are made -- it isn't a decision the tracking system should be making on your behalf.