Adelaide set the tone right from the kick-off when they went forward and had two shots inside the first 60 seconds.
Straight afterwards Alessandro Diamanti set up Berisha with a lovely pass at the other end but the A-League’s record goalscorer could not get a shot away and Adelaide managed to scramble it to safety.
Two minutes later Berisha should have opened the scoring when Max Burgess’ clever header to Diamanti gave the Italian the chance to set up Berisha but the striker could only send his lob wide.
These two misses were to prove costly in the ninth minute when Adelaide forward Nikola Mileusnic found George Blackwood, who drove into the penalty area before firing over a cross which Filip Kurto could only parry.
Mileusnic reacted quickest and slammed the rebound home to notch his fourth goal of the season.
Three minutes later Berisha levelled things up with his 125th career goal.
Burgess went past Adelaide’s Ben Halloran and accelerated forward before finding the Kosovan international who fired past Paul Izzo.
Parity did not last long as Adelaide went 2-1 up in the 15th minute when James Troisi found Blackwood out wide. The striker crossed into the path of Mileusnic, who slammed his second into the roof of the net.
Three minutes later the Reds had stretched their lead, and this time it was Riley McGree who was on target, getting on the end of Halloran’s cross from the right to shoot past Kurto.
Adelaide then threatened to run away with the game as they took control, with Troisi being given too much time and space in midfield to prompt attacks.
Diamanti’s cross had Izzo scrambling to clear from under his crossbar on the half-hour mark and Jerry Skotadis then shot wide.
But Berisha gave the hosts hope two minutes before the interval when he got his second of the game following a neat one-two between Connor Pain and Burgess. The former drove over a cross, Berisha timed his run between the two Adelaide centre backs and bundled the ball home.
Diamanti, so often Western’s talisman this season, got them back on level terms in the 54th minute with a classy left-foot strike from just inside the penalty area after he had been found by Skotadis.
Konstandopoulos was to apply the killer blow, however, leaving Western clinging on to sixth place, a point ahead of resurgent Brisbane Roar.
A rueful Western United coach Mark Rudan could only shrug his shoulders about the way in which his team got back on level terms at 3-3 before crashing to a late Adelaide winner.
”It was an incredible game, it was crazy at times,” he said, describing Western’s first 45 minutes as the worst he had seen his club play during its short A-League history.
Rudan admitted that his midfielders and defenders did not press and defend as a block and allowed Adelaide to take control of the game, especially in the first half.
”Adelaide played through us, they were very good. They were very good at identifying space, they picked their moments and had a bit of quality.”
Michael Lynch is The Age’s chief soccer reporter and also reports on motor sport and horseracing