Just four minutes later a deflection by Tengku Ahmad Tajuddin bounced off Andy Hayward and past Devon Manchester in goal to put the Kiwis two goals behind.
Arun Panchia looked to have scored in the 53rd minute but was called back by umpire John Wright of South Africa for a foul on his defender.
The Black Sticks finally had some luck in the 65th minute with Shay Neal pulling off a stunning full body dive to deflect in Hayward's pass from the side's second penalty corner of the game.
New Zealand lifted in intensity over the final 10 minutes in search of an equalising goal, but Malaysia's defence rallied and remained strong.
The Black Sticks will use Monday's rest day to reassess their tactics before heading into a must-win against Korea at 9pm (NZ time) on Tuesday.
New Zealand 1 (Shay Neal)
Malaysia 2 (Chua Boon Huat, Tengku Ahmad Tajuddin)
Halftime: 0-0