The home side outscored the visitors from Argentina six tries to three in the bonus-point victory in which Beauden Barrett, Dane Coles and Ben May also crossed the line.
Savea slid over in the left hand corner twice in the final three minutes of the first half to flip the contest in the Hurricanes' favour.
Flyhalf Beaden Barrett scored the opening try for Hurricanes in the seventh minute, but the Jaguars' bulk and strong defence pushed them back into the contest.
Hurricanes flanker Ardie Savea, who had chipped through for Barrett's opening try, was sent to the sin bin for dragging down a maul and Jaguars' number eight Leonardo Senatore made the most of the extra space to wrestle over in the 22nd minute.
Ardie Savea returned after his 10 minutes on the sidelines, but it was the Jaguars who scored the next try as a looped pass by scrumhalf TJ Perenara was easily intercepted by centre Matias Moroni, who sprinted 65 metres to score.
The Jaguars, who had lost four matches since winning on their Super Rugby debut, looked set to go in 12-7 ahead at the break, but good work by Barrett created space for Julian Savea to cross in the 38th minute.
There was still time for the re-start and a dart from Perenara followed with a kick ahead set Savea clear to slide over in the same corner with Barrett converting to send the hosts in 21-12 up.
Jaguars flyhalf Nicolas Sanchez slotted an early penalty in the second half to cut the lead to six points but the Argentines were guilty of dropping too many balls and turning over possession.
The Hurricanes captain Dan Coles made them pay in the 57th minute after stepping inside his man and darting in, while a massive shunt by the pack turned over a Jaguars scrum and a long pass found Julian Savea, who dived in for a third try shortly after.
The Jaguars scrumhalf Martin Landajo crossed for a try 10 minutes from time, but the Hurricanes grabbed the bonus point after replacement prop Ben May barrelled over after the buzzer to make it three straight 40-point wins.