The Waratahs got off to a flyer on Saturday night, leading 14-0, and looked in great shape to back up their win over the Highlanders, which ended 40 straight losses for Australian teams against Kiwi foes.
The game was closer than the scoreline suggests, with just two points separating the teams with five minutes remaining.
But Chiefs playmaker Damian McKenzie scored his second try after the final siren to claim a bonus-point win and ensure the Waratahs left empty-handed.