The Hurricanes moved ahead of the Highlanders on the points table to fourth in the Australasian group with 40 points, while the 2015 champions have 38 as they finished within seven points.
In a match that was billed with implications for Steve Hansen's All Blacks squad naming on Sunday, both sides showed the skill level and speed Warren Gatland's Wales team will need to contend with next month.
Despite constant drizzle that made the ground and ball slippery, both teams were prepared to throw it around and trust their players and much of the handling errors came with the ball being slapped free by defenders rather than poor skills.
The Highlanders even produced a trick play worthy of a highlights reel when flyhalf Lima Sopoaga turned his back to the defenders and produced an overhead kick into space that centre Matt Faddes gathered at full speed.
Only a desperate covering tackle from Savea stopped what would have been a try the 19,918-strong crowd would have been talking about for months to come.
Despite their willingness and enterprise neither side was able to truly stamp any early authority on the game.
The Hurricanes, however, proved just how dangerous they can be when openside flanker Savea finished off a sweeping movement from a defensive scrum inside their own 22-metre area.
Fellow loose forward Brad Shields extended the lead from an expertly worked scrum move close to the Highlanders line that sucked in defenders and relied on fast ball to give the blindside flanker the space he needed to crash over.
The Highlanders, who found much of their attack thwarted by a scrambling Hurricanes defence, managed to finally breach their line when quick ball from an attacking scrum allowed Malaki Fekitoa and Patrick Osborne to get some go forward and Sopoaga to run through a disorganised defence to score.
Trailing 17-7 at halftime the Highlanders began the more organised in the second spell with their close quarters interplay leading to a try to prop Dan Lienert-Brown and a Sopoaga penalty to tie it up at 17-17.
Beauden Barrett and Marty Banks then swapped penalties to leave the score locked at 20-20 until Savea burst his way through in the final minute following a sustained period of pressure from the home side.
Original source: Savea saves Hurricanes with last minute try