Djite injured his groin and hobbled from the pitch just 80 seconds into the clash with Argentine striker Neumann his replacement and earning more game time than he has for more than a month despite already having four goals to his name this season.
He made an immediate impact in the first half scoring in the 29th and 37th minutes with the second particularly impressive coming off an outstanding pass from Dario Vidosic.
That put Adelaide 2-0 up despite the Glory actually creating plenty of chances themselves but being unable to get past Eugene Galekovic.
The result was then all but decided just a minute after half-time when Iain Ramsay put the Reds 3-0 up. Even though the Glory scored two goals late through Shane Smeltz (penalty, 90th minute) and Steve McGarry (92nd minute), Adelaide banked a crucial three points.
The win moves Adelaide back to within a point of the top-placed Central Coast Mariners and keeps them six clear of the third-placed Melbourne Victory.
Adelaide coach John Kosmina was happy enough with the victory after the match.
"We struggled a little bit early on and Perth is a team that is going to put good pressure on you. Given we made a couple of changes we were a little bit nervy at the beginning, but we settled down and got a lucky break with a goal although we might have deserved because of the pin-ball incident not long before that," Kosmina said.
"We then got a well-constructed second goal with a great run from Jeronimo after a great pass from Dario. We went on with it in the second half and that was good, but maybe we should have made more of our opportunities.
"I don’t think that was a pen. Smeltzy had lost control of the ball and I've seen him do it 100 times. He ran into Golik, Golik didn’t run into him. That gave them a sniff probably."
It was a disappointing result for the Glory, though, who now are just clinging to a spot in the top-six currently in fifth jut a point ahead of Melbourne Heart, and only two in front of Brisbane and Newcastle.
Glory coach Ian Ferguson certainly didn’t feel his team deserved to go down 3-0, but some of Perth's problems are at their own doing like conceding soft goals and not converting chances.
"To go 2-0 down right on half-time I just couldn’t believe it. I thought the boys did really well in the first half and we had a few good chances ourselves, but we allowed them to score some really silly goals," Ferguson said.
"There was a gap there for their second goal that you could drive a bus through so I wasn’t happy at all with them at half-time, but they showed good character in the second half.
"The goal that killed us came just after half-time from a set piece but they showed good character after that and never gave up. They kept going right to the final whistle and it was a perfect example why you don’t give up because goals can come very quickly, and games change very quickly."
Round 16 of the A-League continues on Saturday with the Melbourne Victory hosting the Central Coast Mariners, and the Newcastle Jets taking on the Brisbane Roar. Then on Sunday, the Wellington Phoenix hosts the Western Sydney Wanderers, and Sydney FC faces Melbourne Heart.