The decisive blow in the thriller came in the 74th minute when the video assistant referee adjudged Glory defender Scott Neville had blocked Kaludjerovic's volley with a hand.
The penalty was eventually awarded, Kaludjerovic converted and Wellington opened out a two-goal lead in the action-packed end-to-end match.
Kaludjerovic extended the margin in the 87th minute, heading home Adam Parkhouse's cross to grab a brace and boost his tally to five goals for the season.
The win over fifth-placed Perth finally shifts Wellington off the bottom of the ladder into eighth place, adding a much-needed three points to their two draws and three losses for the season.
However, the early omens were ominous when Perth opened their account after just nine minutes.
Marco Rossi's back pass put Nix keeper Keegan Smith under pressure, the youngster taking a heavy touch and conceding the indirect free kick when he handled the ball as Andy Keogh loomed.
Perth capitalised clinically, Diego Castro laying off for Xavier Torres to slam home into the top right corner.
Stung, Wellington hit back just four minutes later, Fijian international Roy Krishna featuring with a sharp turn and inch-perfect ball for Dario Vidosic to nod home.
Krishna shone again in the 34th minute, the Fijian pouncing on a loose pass from Neville before setting up Goran Paracki's smart right-foot finish.
Although they took a 2-1 lead into halftime, Wellington lasted barely two minutes from the restart before conceding again from a quick short corner, Shane Lowry heading home from the near post to level the scores.
From then on it was all Wellington. They grabbed the lead back five minutes later, Gui Finkler turning onto a beautiful Krishna pass in the box to slot home with his second touch before Kaludjerovic wrapped up the win with his brace.