The Sky Blues also conceded two own goals in their worst ALW loss, with Bev Priestman's Phoenix needing less than three minutes to open the floodgates at Porirua Park.
Moving to seventh, Wellington (2-2-2) will hope Saturday's demolition job will kick-start their climb up the table.
"We have to kick on," Priestman told Sky Sports.
"I was really pleased more than anything, we kept the clean sheet as well.
"That's the standard that we have to set for this team.
"We've got to stay humble and hard-working."
Sydney FC drop to sixth (2-3-2) after suffering their biggest defeat since a 6-0 away loss to Melbourne City in 2015.
The Sky Blues will have to lick their wounds without captain Nat Tobin, after the veteran defender announced her pregnancy earlier in the week.
Manaia Elliott was the first to get on the scoresheet, before star striker Bhandari added to the buffer in the 13th minute.
Phoenix midfielder Brooke Nunn had set up Pia Vlok in the box, with Sydney goalkeeper Tiahna Robertson spilling the ball.
Elliott pounced on the crumbs to find the back of the net, before Nunn popped up again with a quality cross from the right wing to set up Bhandari's headed goal.
It was Bhandari's first of the season, with the Nepalese captain quickly earning cult figure status.
Wellington's ascendancy couldn't be stopped, with New Zealand international Jale reacting quickest in the box on 36 minutes after a corner kick.
Jale again made the most of a corner kick to complete her double in the 54th minute, before Bhandari pulled off the same feat in the 69th.
Just when Sydney FC thought an own goal - given away by Tori Tumeth in the 80th minute - was the final nail in the coffin, stand-in captain Sarah Hunter gifted the 'Nix their seventh.
Lucia Leon's shot at goal had deflected off Hunter and into the gloves of Robertson, but the keeper dropped the ball over the line.
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