In-form striker Speckmaier scored her 10th goal of the season when Macey Fraser hassled Nanako Sasaki off the ball, allowing the Venezuelan to score from the top of the box.
Speckmaier is now three goals behind golden boot leader Michelle Heyman.
Isabel Hodgson had Adelaide’s best effort on the half-hour mark, saved exceptionally by Rylee Foster in the ‘Nix net.
After a faulty sprinkler caused a longer-than-usual halftime break, Wellington pushed on with Alyssa Whinham striking the post with a mighty volley.
Within minutes, the contest was out of sight. Taylor was in the right spot to lash a volley home from Isabel Cox’s miscontrolled effort.
Wellington’s third was a thing of beauty, with a piece of superb Cox trickery starting a move that saw Main running free to cross for Robertson to tap home.
Robertson then turned provider for an added-time fourth, sending a low cross to the back post where Foster lashed into the net.
The equation for the Phoenix, now eighth with 25 points, to make the finals is simple.
First, they must hope sixth-placed Western Sydney (30 points), slip up when they host second-placed Western United on Saturday.
Then, Wellington must win in Canberra on Sunday.
Those results would open the door for a straight shootout the following Saturday when the Wanderers visit the Kiwi capital.
Also in the race are Newcastle, currently seventh with 27 points, with assignments against Melbourne Victory (H) and Adelaide (A) to close out their campaign.