The Chiefs claimed four points to remain within reach of the top two ahead of the final round of Super Rugby Trans-Tasman fixtures.
The Chiefs did their best to produce a stunning comeback, but the Reds held on to secure a hard-fought victory.
Richie Mo'unga shone as the Crusaders, winners of Super Rugby Aotearoa, thrashed Australian champions the Reds in their Trans Tasman clash.
Tense finishes went in the favour of the Crusaders and the Chiefs in Super Rugby Trans-Tasman, while the Blues were emphatic victors.
Richie Mo'unga won his kicking battle with Damian McKenzie as the Crusaders triumphed in the Super Rugby Aotearoa title match.
The Chiefs were much-changed for their Super Rugby Aotearoa match against the Blues, who still had to work hard for a 39-19 victory.
The Hurricanes appeared set to clinch just their second win of the season, only to be beaten by a last-gasp penalty on Friday.
Just one point separated the sides in Hamilton, with Damian McKenzie's late penalty sending the Chiefs into second place.
Sam Cane has vowed to come back stronger after the New Zealand captain went under the knife.
History was made on Saturday, as the Chiefs secured the first-ever golden-point victory in Super Rugby Aotearoa.