United bossed the contest from start to finish with Juan Muniz opening the scoring on 12 minutes with a sweetly struck free kick.
Jonny Yull made it 2-0 on 29 minutes before Luka Jovanovic capped off a stunning team move with Adelaide's third, three minutes into the second half.
Substitute Luke Duzel iced the victory with a brilliant solo effort in the 91st minute.
While the Reds have notched some impressive wins this campaign, including a 4-1 rout of Melbourne City, as well as dramatic late victories against Melbourne Victory, Brisbane Roar and Sydney FC, Andrioli preferred United's almost faultless dismantling of Perth.
"Yeah, I think it was," he responded, when asked if it was the Reds' most complete display of the season. "We put in a very good performance tonight, not just the result, but the way we played.
"All the stuff we've been talking about, we can probably say came together tonight.
"Playing with belief, players having the freedom to express themselves and to do things they know they can do."
Andrioli is hoping United take this form into their clash against fierce rivals Melbourne Victory at AAMI Park on Friday night.
"People see the freedom, the creativity, but there was a lot of discipline in the structure and the jobs that each individual had to do," he said.
"It's about doing the little things well, playing with that discipline and then individuals shine, and collectively as a team.
"For us now, we regroup, prepare this week and see if we can do the same next weekend."
Glory coach Adam Griffiths urged his side to put the poor performance behind them and focus on the week ahead.
Perth take on Brisbane Roar in Brisbane before back-to-back fixtures across the ditch in New Zealand against Auckland FC and Wellington Phoenix – a run of four consecutive away matches.
"I think after a performance like that, I would just be desperate to get back onto the training pitch and correct what just happened there," he said.
"We knew if we got the first goal in the second half we were going to have a shot of coming back into the game but we conceded in the first two minutes."
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