Hamish Watson secured the points and pushed Wellington into third place with a sharp twist and turn on the edge of the box before firing home in the 86th minute.
Canterbury United moved level with Auckland City at the top of the table after cruising to a 2-0 win over Wanderers SC in Christchurch.
A goal either side of halftime from Russell Kamo and Michael White was enough to earn Keith Braithwaite's side their third win on the trot.
A trying week for Hawke's Bay United ended in a resounding 6-1 win over Southern United at Forsyth Barr Stadium on Saturday.
After having three points deducted for playing an unregistered player against Wanderers SC, and subsequently falling from second to fifth on the league table, six goals from Aaron Jones, Nathaniel Hailermariam (2), Tom Biss, Bill Robertson and Harley Rodeka put their play-off push back on track.
In Hamilton a late first-half free kick from Emiliano Tade and a last-minute clincher from Darren White was enough to give Auckland City a deserved 2-0 win over a plucky WaiBop United side.