Hayman had to take over the No 2 singles spot but was beaten in straight sets by Katherine Ip 6-2 6-2. She rebounded with Guthrie in the doubles as they beat Ip and Venise Chan 7-6 6-4.
It got better overnight yesterday, as the Kiwis easily beat Turkmenistan 3-0 without dropping a set.
Hayman beat Guliahan Kadyrova 6-0 6-0, then she and Guthrie were 6-4 6-1 winners over Anastasiya Prenko and Jenneta Halliyeva.
They play Singapore in their final pool match.
To have a chance of finishing top of their pool they must win the match-up and hope Hong Kong lose their final contest.
The winner of the pool will face the victors in the other pool, with the overall tournament champions gaining a spot in Asia/Oceania Group I for 2014.