The Jaguares still led a crazy game until the 71st minute before running out of energy - and players - and letting in three late tries.
For the Hurricanes, Savea was one of five players, including his brother Julian, All Blacks Cory Jane and Victor Vito, and prop Chris Eves, who were dropped for the Hurricanes' most-recent match against the Queensland Reds after missing a team curfew during a South African tour.
He made an outstanding return Friday, scoring the opening try, then crashing through the Highlanders' vaunted defense for the decisive score in the last minute of the match.
"We had to go to the bottom of the barrel for that one," Hurricanes captain Dane Coles said. "We knew we had to keep hanging in there for 80 minutes."
At Sydney, the New South Wales Waratahs increased their lead in the Australian conference to five points over the ACT Brumbies with their win over the New Zealand conference-leading Chiefs.
Center Folau raced 90 meters for an early intercept try against the run of play, then clinched victory with his second five-pointer in the 64th minute.
The Chiefs' loss tightened up the New Zealand conference standings, with just four points separating the top four teams. The Chiefs have 42 points, one better than the Crusaders, who play the last-place Blues on Saturday in Auckland.
The Hurricanes are in third place, one point behind the Crusaders, and two ahead of the Highlanders.
Down to 13 men from the 37th minute, and 12 men for the last 10 minutes, the Jaguares lost it late as they let in a penalty try and scores by Dewald Human and Wandile Mjekevu.
No. 8 Facundo Isa scored a close-range try and flyhalf Nicolas Sanchez landed five penalties for the Jaguares, but they ultimately paid for their indiscipline.
Lock Thomas Lavanini was sent off in the 25th after a shoulder charge to the head of a Kings player at a ruck.
The Jaguares had a try disallowed because of Lavanini's foul play in the buildup. Prop Ramiro Herrera was also given a red card for the same offense 12 minutes later, when he charged into the back of the head of Kings captain Steven Sykes. Flanker Thomas Lezana was sin-binned late on.