Both sides created further chances but failed to make them count in an open first half.
The 50th minute marked the turning point, when WaiBOP United's Wade Molony was shown a red card.
Team Wellington were on level terms through a Bill Robertson header 10 minutes later, before Michael Gwyther completed the recovery with 18 minutes remaining.
WaiBOP United coach Peter Smith left little doubt about his feelings.
"We changed things today, played some good football and were well worth our lead," Smith said after the match.
"But then Wade gets sent off and the game changed, through little fault of our own. I can't comment on the red card, apart from saying I'm very, very disappointed with certain aspects of it."
Smith said there were plenty of positives to take from the side's second straight loss.
"Despite the result we played well, created chances and put them under pressure. We had it in our hands to beat one of the big boys, so not to be able to do so is probably the most disappointing thing.
"The players didn't deserve to lose, but that's the way it goes. We did great with things we could control. It was something we couldn't control that let us down."
Wellington coach Matt Calcott was happy to get the points and said there was still plenty of improvement left in his side.
"At halftime I said we need to play with a bit more intent and a bit more passion and that's what they did in the second half and that was probably the difference.
"I'm really happy that we've come from behind but I'm not happy with the defending at times. But if we play like we played in the second half over the course of the full 90 minutes, we will go well."
