The flanker replaced the injured Sean O'Brien just before half-time and produced a powerful performance that featured a turnover, seven tackles and eight carries for 30 metres.
Leavy, 24, was a delayed arrival into the Ireland camp after playing a full 80 minutes for Leinster against Southern Kings in Port Elizabeth the previous Sunday.
Ireland's Kiwi coach Joe Schmidt was certainly not ruling it out in the wake of his team's unconvincing 28-17 victory over Argentina at the weekend, though he admitted it was "unlikely".
"It was a real Test match, really arduous", said Schmidt.
"I always remember the 2013 game and it was one of the toughest matches I had just in terms of the physicality and the breakdown work that went on".
Schmidt guided Ireland to two Six Nations titles before going one better with the Grand Slam this year - only the third in their history in either the Five or Six Nations championship - after winning two European Cups and a Pro14 trophy with Leinster.
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Schmidt told reporters there was "no compulsion to push himself forward or to come out and try to force himself into the frame, unless he's super comfortable". "You want to play against the best teams in the world and have a shot at them".
"I don't think it really spills over into the narrative", he said. New Zealand will put us under a lot more pressure and it's a massive challenge for us but that's why we play Test rugby.
Hansen and Schmidt will probably avoid each other for much of the coming week as they prepare their sides for the clash between the world's two top-ranked sides in Dublin on Sunday morning. Josh has been playing really well, all the boys in Chicago had serious games.
"They will say they were 15-0 down (against England) and didn't start well but came back and they will see we also didn't begin well but also fought back".
"From a player's point of view, and even from an Irish rugby fan's point of view, you want to see the best coaches staying and he's the best coach I've ever worked with", said Best. On that occasion, Ireland stormed to a 40-29 victory in Chicago, before New Zealand bounced back to win 21-9 in Dublin.
"And I know Ireland will be a better team when they play us because everyone seems to find another 10 per cent when they play us because it is a good story if you can beat the All Blacks and everyone gets excited by that".