Two goals to in-form striker Nikita Rukavytsya gave the Glory a 2-0 win after a sluggish start in what was a vital match for the club.
“It was a very important game and it showed with the players being very nervous in the first half,” Perth coach Dave Mitchell said.
“We couldn’t string too many passes together even though we went 1-0 up. I had a few stern words with them at half-time and the second half was a much better performance.
“We are just above Wellington now and hopefully we can get a couple of more results, particularly at home.”
Wellington replace Perth at the foot of the table but only one point separates the pair and both sides are still within striking distance of the top four.