Matu'u's try was down to the genius of Beauden Barrett as a pinpoint grubber kick from the pivot produced the perfect bounce for the burly hooker to run on to and dot down in the same corner that Goodes had scored in only minutes earlier.
Goodes was only a late call-up to start the game after Ben Franks was scratched due to a lower back problem.
When Savea scored his second of the game, the victory looked safe at 38-19 with 24 minutes left.
But Hurricanes fans have long dealt with knowing a contest involving their side is never over until the final whistle and the Waratahs threatened to spoil the party as Adam Ashley-Cooper scored mid-way through the second spell to bring the score to 38-24.
Barrett then iced the contest as he knocked over a penalty from close quarters with eight minutes left to contribute to his personal points haul of 21 as the Hurricanes closed out the game comfortably, despite a late try to Waratahs fullback Israel Folau.
Earlier, Waratahs first-five Bernard Foley produced the most exciting patch of play during the first 40 minutes as he received the ball from a ruck then scythed through four would-be Hurricanes tacklers on his way to an impressive individual try.
His five-pointer cancelled out the earlier effort of Savea, who grabbed the first try of the game in the 13th minute when he finished off a sweeping move from the Hurricanes after they recovered a TJ Perenara box kick.
Savea's younger brother, Ardie, who was making his Super Rugby debut, also had a hand in the try and was generally busy during the opening exchanges, while his support play was handy.
Aside from those two tries, the first spell largely entertained a kicking duel between Barrett and Waratahs halfback Brendan McKibbin as both sharp-shooters found their range from the tee despite the damp conditions.
Barrett had the final say of the first half though as his fourth penalty _ with the hooter blowing in the background _ gave the home side a slender three-point advantage at the split that they would never relinquish due to their clinical second-half display.
Hammett needs to find a way to tighten up his side's backline defence and eradicate a few dropped balls but his team are building nicely as the Super Rugby season starts to heat up.
Next Saturday, the Hurricanes head north to meet Sir John Kirwan's Blues in Auckland and they will have revenge on their minds after they were beaten 34-20 in round two by Kirwan's side.
Hurricanes 41 (Julian Savea 2, Reg Goodes, Motu Matu'u tries; Beauden Barrett 5 pens, 3 con) Waratahs 29 (Bernard Foley, Adam Ashley-Cooper, Israel Folau tries; Brendan McKibbin 4 pens, con) HT: 19-16
