The 28-year-old striker, who missed Australia's run to the Asian Cup Final earlier this year with a back problem, made the most of a mix-up in the 10th minute and slack defending in the 59th to score his eighth and ninth international goals.
Local midfielder James Troisi later capped a fine performance by rounding off the scoring with a penalty deep into injury-time.
Weakened by injury and jet-lagged after their journey from the United States, where they lost 3-0 to Mexico on Wednesday, New Zealand created precious few scoring chances and the profligate Socceroos should have won more convincingly.
Coach Holger Osieck, whose charges beat his native Germany in March, was satisfied with an eighth win in 13 matches since he took over last year, particularly in the absence of Tim Cahill, Harry Kewell and Mark Schwarzer.
"There were a lot of positives and I got what I wanted to see," he said in a televised interview. "I think overall apart from the score and the overall performance, I think today I found a lot more depth for the future.
"We created some excellent stuff up front but we weren't clinical enough to finish and that is definitely something I dislike," he added.
Kennedy had a couple of glaring misses but made no mistake when a miscommunication between All Whites Jeremy Brockie and Glen Ross allowed him to disposess goalkeeper Ross and fire the ball into an empty net after 10 minutes.
Forward Chris Wood blasted New Zealand's best chance over the bar just after the break before Kennedy rosed unmarked to double the lead with a free header from a Dario Vidosic corner just ahead of the hour mark.
New Zealand were well beaten by the time Ben Sigmund brought down livewire striker Robbie Kruse three minutes into injury time to allow Troisi his moment of glory in front of his hometown fans.
Australia face Serbia in Melbourne on Tuesday as they contine their preparations for the start of the campiagn to qualify for a third successive World Cup finals in 2014.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
