A 29-23 victory on Saturday at Dunedin's Forsyth Barr Stadium came without rested captain Tate McDermott, injured star flankers Liam Wright and Fraser McReight (both shoulder) and Test hooker Matt Faessler (leg).
The visitors defied some early pressure to lead 12-0 before conceding 20 straight points when unforced errors and missed tackles crept in.
But the Reds, energised by a bench led by reserve prop Alex Hodgman and fit-again lock Lukhan Salakaia-Loto, turned to their scrum in a pulsating second-half effort that moved Les Kiss's side to 4-1.
It was their first win at the venue since their inaugural fixture there in 2013 and just the Reds' third win in New Zealand, against Kiwi opponents, in their last 27 games.
"Other sides come at you but we are getting better at coming back on track in games," Kiss said.
"We stretched into our depth but we know we have players who step up."
In his first game as Reds captain, Wallabies skipper Harry Wilson was inspirational.
He plucked a crucial late turnover with a heads-up play and routinely dented the line, while adding a deft kick ahead that led to the Reds' decisive final try.
"It's very special. We've talked all week about 2013 and being a side that could re-write the history books there," Wilson said.
"We were pretty disappointed at halftime, thought we didn't play our brand of footy. And the scrum changed the game."
Outside centre Filipo Daugunu scored twice and was formidable in defence, the Reds following his lead to produce consecutive turnovers once they hit the lead with 17 minutes to play
But it was their scrum that made the difference, the Reds showing newfound in-game awareness to bank on their set-piece superiority that yielded four penalties inside 11 minutes.
That led to a yellow card for All Blacks prop Ethan de Groot, who felt the pressure and gave away a penalty at the breakdown and created the Reds the platform to surge clear.
Tries to winger Lachie Anderson and Daugunu - the latter's coming after Tim Ryan sped through the line and Wilson kicked ahead - put the Reds clear.
The host's only second-half points came courtesy of penalty kicks, the second of those after the bell with victory out of reach.
Their inability to penetrate was at shocking odds to their first-half form, when scintillating winger Caleb Tangitau burst out of the blocks.
Denied a brilliant first-minute try when his chip ahead narrowly went into touch, the former rugby sevens star was robbed of another when replays showed an accidental offside in the build up.
They led 17-12 at that stage, Reds fullback Heremai Murray yellow-carded for a deliberate knock down to leave the visitors reeling.
Tanielu Tele'a and captain Timoci Tavatavanawai had already crossed for the Highlanders, who had forced five consecutive penalties out of the Reds and were calling all the shots.
But the visitors showed tremendous resolve to stop the bleeding and then turn the screws after the break to earn a bonus-point win.
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