Damian McKenzie scored a try and kicked 15 points, the last of which were from a conversion that went in off the post in the dying seconds, to give the Chiefs a dramatic win over the Jaguares in Buenos Aires.
Centre Tumua Manu also scored a try for the Chiefs, who were 17-6 up at the break and increased the lead to 20-6 minutes after the restart before the Jaguares roared back in the second spell.
Converted tries to Joaquin Tuculet, Pablo Matera and Matias Orlando gave the home side a 27-23 lead with just seven minutes remaining.
But a last-gasp try by replacement scrumhalf Te Toiroa Tahuriorangi, converted by McKenzie, gave the visitors the win and kept the Jaguares rooted to the bottom of the South African conference.