He came off the bench to replace Ivan Vicelich, and nodded home his first ever international goal to seal the 2-1 World Cup qualifying win.
The reverse fixture will be played in Wellington on Wednesday, and Mulligan is desperate to regain his place in the starting line-up having been left out fot this clash.
"To be dropped for your country is not a good thing," he told nzsoccer.com.
"When I heard about it I was quite down, but to come on and score the winner is the best answer I could have given. Hopefully now I can push for a start in Wellington."
Iron goalkeeper Murphy was on the bench for the Republic of Ireland as they drew 2-2 with Wales at the Millennium Stadium in Cardiff.
And Paterson failed to get on the pitch at Windsor Park as Northern Ireland kept their Euro 2008 qualifying hopes alive with a 2-1 win over Denmark.
Warren Feeney and David Healy scored the goals for Nigel Worthington's side, who will head to Switzerland and Austria if they beat Spain on Wednesday and Latvia claim a surprise win in Sweden.