Senior Constable Bruce Dow said a 39-year-old man and a 17year-old youth were caught out by the "oldest trick in the book".
Police were called about 3.15am after a burglary at the Itchen Street Dairy and followed the trail to Orwell St, where the two were apprehended.
Dairy owner Kerry Tong, who lives above the store with his wife and two young children, said he was woken by the sound of someone trying to break the shop's front window.
But he found the window intact and no sign of any offenders.
After he had returned upstairs, he heard glass breaking, so called police.
He watched two men fleeing with two boxes of ice creams.
Mr Tong, who moved to Oamaru with his family four and a-half years ago, said he was "scared we would be hurt".
The pair have been charged with burglary and released on bail.
