The Killik Cup clash will see Savea's younger brother Ardie line up for New Zealand.
It was the 11th meeting between the teams since their first match in 1954 and the All Blacks have won eight of them.
New Zealand came in to the game on the back of defeat by Australia and were looking to get back on track ahead of their tour games against France and Wales.
Luatua excited the crowd again with another intercept but, lacking the confidence to charge on, failed to find his supporting teammates.
This time Mo'unga did convert and the Barbarians led 17-5.
Barrett missed the conversion but come the 53rd minute New Zealand was level when centre Laumape surged through Mo'unga's tackle after taking a flat pass off a five-metre scrum for a converted try.
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Man of the match: Harold Vorster and Richard Buckman made for in interesting midfield combination, while Steve Luatua was the power of the BaaBaas' pack.
The Barbarians even showed they could play some traditional footy, too, when big Sam Carter powered over for their third try from some nice ruck-and-drive action, and they must have been delighted to take the seven-point cushion into the sheds. Some sloppy interplay followed, but the BaaBaas managed to regain control of the ball and it resulted in a try for George Bridge.
All Blacks 31 (TJ Perenara, Vaea Fifita, Ngani Laumape, Sam Cane, Nathan Harris tries; Beauden Barrett 3 cons), Barbarians 22 (Richie Mo'unga, George Bridge 2, Sam Carter tries; Mo'unga con).
Replacements: A van der Merwe (Lions), B Franks (London Irish and New Zealand), R Smith (Toyota Verblitz), W Britz (Sunwolves), R Ackermann (Gloucester), M Drummond (Crusaders), R du Preez (Stormers), D Hunt (Highlanders).
Having started like a house on fire, the Barbarians exuded confidence throughout the first half, scoring two well worked tries to lead a lackluster All Blacks side 17-10 at the break.
There was time for new chums Asafo Aumua, Tim Perry and Matt Duffie to enter the fray late for their first appearances in the black jersey.