Persist reads: 'When this creature dies, if it had no -1/-1 counters on it, return it to the battlefield under its owner's control with a -1/-1 counter on it.' The keyword 'dies' means the creature was moved from the battlefield to the graveyard (CR 700.4), and this includes being sacrificed.
Sacrifice is simply a way to move a permanent from the battlefield to the graveyard as a cost or effect (CR 701.17). It is not the same as destruction, but persist doesn't care about the method of dying — only that the creature died and had no -1/-1 counters on it at the time it left the battlefield.
The persist ability is a triggered ability that checks a condition at the moment of death (CR 702.79). As long as the creature had no -1/-1 counters when it went to the graveyard, persist will trigger whether the creature was destroyed by a spell, killed in combat, or sacrificed to an effect.
Example: You control a Murderous Redcap (which has persist) with no -1/-1 counters. You sacrifice it to Goblin Bombardment to deal 1 damage. Persist triggers, and Murderous Redcap returns to the battlefield with a -1/-1 counter on it — ready to be sacrificed again for another 1 damage.
Note: If the creature already had a -1/-1 counter on it when it was sacrificed, persist will not trigger, regardless of how it died (CR 702.79a).
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.