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.
The win comes amid speculation over Aloisi's coaching future, with the Socceroos great considered an outside chance in the Matildas' coaching race, and also attracting interest elsewhere in the A-League.
Red-hot 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.
Michael Ruhs teed up fellow substitute Ramy Najjarine to wrap up three points in the 86th minute.
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 and host Auckland in the final round.
United took the lead when Bozinovski had his first shot saved by Oli Sail but buried the rebound in style to earn his fourth goal in three games.
Western have scored more goals this season (48) than any other in their history with four games remaining.
Perth were sharper out of the blocks in the second half, and equalised when Pearman danced along the edge of the area then let rip with a wonderful strike.
But United regained their lead in the 65th minute when Gomulka attempted to block a Bozinovski cross but mis-hit the ball and it wrongfooted the Glory defence to nestle in the back of the net.
United sealed victory when Ruhs burst forward and slipped the ball to Najjarine to score.
Perth return home to face Adelaide next Saturday.
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