Three points took United - playing its debut season - into the top six ahead of Adelaide United on goal difference.
With Adelaide having completed its regular season, Mark Rudan's sixth-placed side need only collect a point or avoid a 15-goal swing in their remaining two matches.
It could yet climb as high as third, leapfrogging Wednesday's fifth-placed opponent Perth in the process, with Berisha in inspired form.
His goals were slightly fortuitous, the first ricocheting in as Liam Reddy flapped at a cross, with the second a penalty early in the second half, but the veteran forward posed a threat throughout.
In the day's late game between two sides playing for the final time in 2019-2020, Western Sydney Wanderers ran out 2-1 winner over Melbourne Victory.
Pirmin Schwegler calmly placed in the opener late in the first half, before Jordan O'Doherty's superb first-time finish doubled the advantage.
Victory quickly responded as Andrew Nabbout was left unmarked and onside in the six-yard box, but it counted for little.