Botic, 23, joined Sydney FC star Joe Lolley (nine goals) at the top of the golden boot standings with a clean finish in the 26th minute at Ironbark Fields on Sunday.
Hiroshi Ibusuki added a second from the penalty spot in the 59th minute before Riku Danzaki sealed all three points in the 88th.
Western coach John Aloisi was delighted with an "angry" Botic's response to going goalless against Auckland FC, but stopped short of saying he should be in contention for March's World Cup qualifiers.
"In terms of the way he's performing, I would love Noah to get selected for this window," he said.
"But if he doesn't, it doesn't mean that he's not going to be a future Socceroo.
"I really do feel that there's so much left in him. This is by no means a finished product of Noah. He's still got a lot to learn, a lot to improve on.
"Then physically he's just starting to get better and better, but he's still, I think, a little bit off in terms of where we think his ceiling can be.
"So if he doesn't get selected, I don't think he should be too upset. He should just keep going and keep moving and keep improving and keep doing well for us and then the other things will fall into place."
In the process, United (29 points) bounced back from a 2-0 loss to leaders Auckland (39) and jumped to within two points of the second-placed Reds.
"Today, we performed really well. It was a great performance from start to finish," Aloisi said.
United were celebrating Aloisi's 100th game at the helm and dominated from the outset, with talented winger Abel Walatee impressing.
It paid off when Matt Grimaldi launched a wonderful crossfield ball to Walatee on the left.
The winger cut the ball back to Ben Garuccio, who cleverly lifted it into the path of Botic to tap home.
Western earned their penalty when Isaias legged Ibusuki in the area and the former Adelaide striker made no mistake from the spot.
The home side sealed victory when Danzaki turned onto his left and fired a shot that slipped through Cox's fingers.
"We weren't good enough, as simple as that," Adelaide coach Carl Veart said.
Western next take on Central Coast away on Friday while Adelaide, who have won just one of their past five and battled injuries, illness and losing players to Young Socceroos duties, travel to Auckland on Saturday.
"It's a little bit of a tough time at the moment, but we have to bounce back, and we have to push forward," Veart added.
"We can't just feel sorry for ourselves. We have to work harder and be better."
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