But it took less than three minutes for David Williams to square the ledger for Wellington, tapping home Louis Fenton's cross from close range to notch his fourth goal in six games.
Wellington were enjoying the majority of possession and at the end of a flowing move which involved 24 passes, Krishna was tripped in the penalty area to win his side a spot-kick. The Fijian himself took responsibility, blasting home his tenth goal of the season to put the Phoenix ahead.
Eight minutes later, he was at it again. Another sweeping move from Wellington ended with Williams drawing a save from Lawrence Thomas but the red-hot Krishna pounced on the rebound to fire in the Phoenix's third.
Late in the first half, Kurto pulled off a crucial stop to deny Barbarouses after he was put through one-on-one and preserve the half-time advantage.
In front of a vocal 18-thousand strong crowd, including the healthiest throng of Wellington Phoenix away fans in recent memory, Melbourne chased the game after the break. It took just ten minutes for James Troisi to reduce the deficit to 3-2, driving into the penalty area to latch onto Toivonen's precise pass and clinically finish. Ten minutes later, Terry Antonis struck the post with Kurto stranded.
Wellington continued to soak up immense Victory pressure with Kurto constantly called into action. In front of him, the Phoenix defence and the outstanding Alex Rufer stretched every sinew to keep their hosts at bay.
Just when it looked as though they would secure just a third win in 19 visits to Victory, the ball fell invitingly in the box to Barbarouses in the 88th minute who made no mistake to break Wellington hearts.
The Phoenix continue a busy week when they host third-placed Sydney FC on Wednesday evening before Melbourne City visit Westpac Stadium on Saturday.
Melbourne Victory 3 (Ola Toivonen, James Troisi, Kosta Barbarouses)
Wellington Phoenix 3 (Roy Krishna 2, David Williams)