After Auckland drew 1-1 with Western Sydney earlier on Saturday, John Aloisi's United seized the opportunity to maintain outright second place with four games to go, beating struggling Perth Glory 3-1.
United's fifth win on the bounce came amid speculation over Aloisi's coaching future.
The Socceroos great is considered an outside chance in the Matildas' coaching race, and is attracting interest elsewhere in the A-League.
United are chasing the premiership but the top Australian team will also earn a place in next year's Asian Champions League Elite (ACL Elite).
As things stand, Auckland (46 points) lead United (41), Melbourne City (40), who beat Central Coast on Saturday, Western Sydney (36) and Melbourne Victory (36).
United travel to face Western Sydney next Sunday, then face Brisbane away and Sydney at home before hosting Auckland in the final round.
"There's still four games left ... the top six are still pretty much alive," Aloisi said.
"So we don't want to talk about Champions League or premiers plate until right near the end.
"We're in a good space at the moment in terms of our results, most of our performances.
"And we just want to keep picking up as much points as we can, because we know that we're going to need the points if we want to finish in that top-two area."
Midfielder Rhys Bozinovski delivered United the lead inside three minutes at Ironbark Fields.
Perth sensation Jaylan Pearman equalised with a wonderful long-range strike in the 55th minute, before Taras Gomulka's calamitous own goal gifted United the lead 10 minutes later.
"The disappointing thing is now we're actually scoring goals, not enough, but those soft goals are just going to kill you," coach David Zdrilic said.
"You just can't keep fighting back from that."
Michael Ruhs teed up fellow substitute Ramy Najjarine to wrap up three points in the 86th minute.
United have 15 individual goal scorers this season, the most of any team in the league.
"It is valuable because it's hard to stop - how do you stop a team that's got 15 different goal scorers?" Aloisi said.
Perth, who play Adelaide at home next Sunday, sit rock-bottom but first-year Zdrilic was adamant the club was backing him.
"I've been very fortunate that the backing has always been there, and from Ross (Pelligra), from Jason (Bontempo) from Stan (Lazaridis), it's always been very positive, and we're in constant communication about all the challenges that we face," he said.
"So, yeah, I feel very comfortable with the support they're giving me, but I also know that this position is one that always comes with that danger."
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