Parma midfielder Marco Bresciano fired Frank Farina's side into a 1-0 lead six minutes before the break with a superb free kick after he himself had been brought down on the edge of the penalty box.
Lazaridis came close to doubling the Aussies lead 18 minutes into the second period but his powerful shot was well saved by Kiwi's keeper Mark Paston.
The Socceroos had numerous chances to extend their lead, most notably when substitute Mile Sterjovski fired over the bar from three feet out in the 85th minute, and in the end had to settle for a single goal advantage over their arch rivals.
Stan went on to complete the full ninety minutes in this his 51st appearance for his country.
Final Score: Australia 1 - New Zealand 0
Australia: Zeljko Kalac, Simon Colosimo, Stephen Laybutt, Tony Vidmar, Stan Lazaridis, Brett Emerton, Vince Grella, Marco Bresciano, Josip Skoko, John Aloisi, Max Vieri. Subs: Scott Chipperfield, Tom Cahill, Alex Brosque, Patrick Kisnorbo, Ahmad Elrich, Mile Sterjovski, Adrian Madaschi, Patrick Kisnorbo, Jade North, David Zdrilic, Brad Jones.
New Zealand: Mark Paston, David Mulligan, Steven Old, Che Bunce, Tony Lochhead, Ivan Vicelich, Noah Hickey, Leo Bertos, Simon Elliott, Vaughan Coveny, Raf DeGregorio. Subs: Duncan Oughton, Aaran Lines, Tim Brown, Brent Fisher, Michael Wilson, Shane Smeltz, Neil Jones, Andrew Boyens, Rupesh Puna, Glenn Moss, Tamati Williams.
Attendance: 12,134
The Socceroos next group game in the tournament will be on Monday afternoon against Tahiti at the same venue.