The Fijian's early strike proved the difference as Tony Popovic's rock-bottom side remain winless, while Wellington sit fourth after making it five matches unbeaten.
Daniel Alessi's 14th-minute foul gave Krishna the chance to break the deadlock from the spot and, though Ante Covic saved the initial effort, the Phoenix forward prodded in the loose ball for what proved to be the winner.
It was just reward for the hosts, who made a bright start and had already called Covic into action with a strong Nathan Burns effort.
Having fallen behind, Wanderers struggled to threaten, though Tomi Juric did go close with a low shot that flew just wide.
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