The Highlanders appeared to be down and out when Sio Tomkinson was sent off for a head-high shoulder charge on Brodie Retallick – who was unable to continue – and Stephen Donald scored the resultant penalty to put the Chiefs seven points up with 12 minutes to play.
However, Josh Ioane hit back with a three-pointer from the tee and Smith wrongfooted the defence on the try-line to dive in for the winning score.
Pari Pari Parkinson powered over to put the Highlanders ahead early on, but Tyler Ardron and Angus Taavao-Matau crossed before Nathan Harris’ brilliant offload sent Etene Nanai-Seturo in at the left corner.
Nanai-Seturo touched down again off a tremendous cross-field kick from Orbyn Leger to send the Chiefs 11 points clear, but Tyrel Lomax’s powerful run and offload enabled Shannon Frizell to reduce the arrears.
Despite Donald punishing Tomkinson’s reckless challenge on Chiefs captain Retallick, Smith found a gap to get Aaron Mauger’s side the victory with four minutes remaining.
Wallabies wing Maddocks capitalised when pressure from Richard Hardwick saw Irae Simone kick the ball straight to him, but Rory Arnold leapt over a ruck to score in response and the Brumbies went into the break leading by three points.
Cooper, who last featured in the competition in July 2017 having been frozen out at the Reds for the entire 2018 season, converted Anaru Rangi’s unstoppable try before Maddocks dived forward to collect Bill Meakes’ kick and dot it down in one brilliant movement.
Sam Carter’s try set up a tense finale, but the hosts were unable to avoid starting their campaign with a home defeat.
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