The hosts played into a stiff wind into the hockey turf end of the park so the key was to keep the ball on the ground but that didn't always happen.
In the third minute, Wellington keeper Jacob Spoonley denied Bay centre-mid Tom Biss a drive at goal in a one-on-one case.
In the eighth minute, the visitors came close to going up from three moves, starting with a long ball from centreback James Musa to the left flank but the pin-point cross into the centre of the 18m box was headed wide under no pressure.
In the 33rd minute, Bay keeper Matt Gould made a blinding save from the ensuing freekick after pivot Charlie Henry's drive curled past the wall towards the exposed segment of the goalmouth.
A minute later, American import Sean Morris missed a sitter from point-blank range in the counterattack, shooting it wide off the right upright with no pressure on him.
If the first spell was cause for consternation, the second half must have felt like a kick in the guts for Greatholder despite the hosts drawing first blood seven minutes into the second stanza after some untidy housekeeping from the Wellington defence.
Centreback Aaron Jones claimed a ball from a free kick spill, turned and slotted it past keeper Spoonley for a 1-0 lead.
Stunned into action, Wellington retaliated seconds after the kick-off to nullify the advantage with a 1-1 equaliser from Henry who latched on to a clearing header from Jones.
The pumped-up Wellingtonians retrieved the ball from the net and ran it to the centre spot.
The Bay had a shot from kick-off but Wellington duffed two opportunities when substitute midfielder Roy Kayara and striker Hamish Watson were guilty of making flower arrangements in the box rather than taking the simple option of a crisp finish in wine country.
In the 61st minute, Watson put Wellington up 2-1 when Kayara pushed a deft pass into the box from the right flank for that finish.
The Bay's defence was a little exposed. Captain Bill Robertson broke the cardinal rule of letting high balls bounce in the areas of contention, enabling nippy customers such as Henry Fa'arodo, Kayara and Henry to pounce on possession with everpresent threats.
In the 86th minute, Kayara could have shut out the match after receiving a great Watson cross from the left flank but he butchered the finish with an errant right foot.
On regulation fulltime, Bay substitute Matt Hastings could have been a hero with an oblique free kick that beat keeper Spoonley but agonisingly hit the crossbar.
"In the second half we didn't hit our stride. It's massively disappointing to take the lead in the way we did and then we had our worst 10 minutes of the game when they obviously scored two goals," Greatholder said, feeling a draw would have been a fair reflection.
He said the players had forgotten to flick off the celebratory switch after the opening goal.
"That's when we're most vulnerable ... it's horrible and the boys will be hurting."
This Sunday the Bay play away against defending Waitakere United at Fred Taylor Park in a 4pm kick-off. Greatholder said his men would put behind yesterday's disappointment and were capable of beating the high fliers if they played to their potential.
Wellington coach Matt Calcott was delighted with the result considering they had lost to Auckland City and Waitakere as well as what he described as a "long day" after they their flight from Wellington was cancelled because of strong winds.
They arrived here about 8pm on a bus trip and left not long after the final whistle from the rescheduled midday kick off.
"Yes we needed to react to the first goal but we also had a good reaction after halftime," Calcott said, adding it's always tricky how a new group of players were going to respond a goal down. The 10-minute passage that yielded two goals was indicative of the side's character.
"It shows the resolve of our guys," he said.
His only criticism of his troops was their inability to finish off potential goals.
