The youngster replaced Marco Tilio with 17 minutes left and was instrumental in the Socceroos' second goal, outpacing the defence in the passage of play that led to fellow debutant Jason Cummings scoring from the penalty spot.
Former Liverpool winger Kewell made his first Socceroos appearance as a 17-year-old in 1996 before going on to represent Australia at the World Cup in 2006 and 2010. Kuol staked his claim for a place in Graham Arnold's squad for Qatar.
Mitchell Duke opened the scoring with a 54th-minute header and Cummings scored from the penalty spot on his debut, as Australia handed New Zealand a defeat in their first game in front of their home fans for almost five years.
It was Kuol's pace that created the second opportunity, the Central Coast Mariners attacker tearing into the area before Riley McGree was denied by goalkeeper Oli Sail and Cummings saw his follow-up hit Liberato Cacace on the hand.
Scotland-born forward Cummings then stepped up to score from the spot and cap a strong second-half showing by a largely second-string Australian outfit, as Arnold made wholesale changes to his line-up after Thursday's win over the same opposition.
The All Whites, who missed out on a place at the World Cup when they lost in a playoff against Costa Rica in June, controlled the first half with Chris Wood, Matt Garbett and Elijah Just all going close.
But the best opening of the half fell to Tilio a minute before the interval, only for the Melbourne City striker to scuff his shot wide with the goal gaping.
Duke made amends nine minutes into the second half when he met Connor Metcalfe's centre with a strong downward header that gave Sail little chance and Cummings put the seal on the win with 10 minutes to go.
Australia will kick off their World Cup campaign, the country's fifth consecutive appearance at the finals, against defending champions France on November 22 before facing Tunisia and Denmark.
