The third-placed Wanderers skipped three points clear of Adelaide, whose off-field pain returned no on-field gain at Hindmarsh Stadium.
After John Kosmina suddenly quit as coach last Monday, the Reds crashed to a third consecutive defeat in a listless display under interim coach Michael Valkanis.
Western Sydney's trumpcard in their fourth win in a row was Ethiopia-born, Netherlands national Hersi, who banked a brace and created a goal for Mark Bridge, while Mateo Poljak also scored.
Reds striker Bruce Djite and Iain Ramsay netted in the second half to briefly appease a restless 9,686-strong Adelaide crowd.
Hersi's attacking flair dominated the fixture and he opened scoring after a goal mouth scramble in the 43rd minute.
Hersi's teammate Aaron Mooy had two rapid-fire scoring attempts, the second going within centimetres of scoring only for Adelaide goalkeeper Eugene Galekovic to flick the ball from the goal line.
But Galekovic's save dribbled into Hersi's path and he duly converted with a neat right-footer.
Just a minute later Hersi, approaching the by-line, hooked a pass to Bridge who was inexplicably left alone on the penalty spot and rifled in the Wanderers' second.
Bridge returned the favour in the 52nd minute when he pinpointed a cross to Hersi, who netted his second goal with a header from one metre out.
Djite temporarily raised the home side's spirits in the 61st minute when he scored from a sweet 15 metre launch.
But Poljak goaled from close-range some seven minutes later for the Wanderers, before Adelaide's Ramsay curled in a low left-footer for a consolation score in the 87th minute.
After the match, Valkanis implored his players to fight to save Adelaide's season which dipped to a new low on Sunday in their listless home loss to the Wanderers.
While still fourth on the ladder, the Reds stumbled to a third consecutive loss and remain reeling from Kosmina's sudden resignation as coach last Monday.
"It has been a very negative week and it has probably finished on the note that it started," Valkanis said.
The caretaker coach said his immediate priority was to keep United united, after the Wanderers skipped three points clear in third spot.
"We need to all rally together and be united and push forward," Valkanis said.
"We need to reinforce some positive outlook into our game and find our feet again ... we need to lift our heads up.
"We have got another eight games - there is enough doom and gloom this week with what has gone on ... we lost the game, we lost the battle, not the war, there is still plenty to fight for."
The Wanderers' stunning debut season continued with a clinical triumph at Hindmarsh Stadium, the newcomers now just one point shy of second-placed Melbourne Victory.
Coach Tony Popovic hailed the "great win" for a club now rated genuine championship contenders.
But he said carrying rising expectations wouldn't burden the newcomers.
"We are a close-knit group, a club that has high aspirations - we want to be the best," he said.
"And slowly we are taking steps forward.
"I don't see it as anything special, it's just the way the Wanderers work.
"And we as a club are very happy with how we play our football, how we conduct ourselves, and moving forward there is a lot more room for improvement on and off the park.
"Now we have shown a great consistency in our results - four straight wins, any team that could achieve that would be pleased.
"But we're not looking ahead too far."