While Burns was forced to take a spot-kick twice to secure his hat-trick, the 26-year-old forward slotted both efforts to be eventually awarded his third goal, which capped off Wellington's impressive home win.
The Phoenix had lost on successive road trip but after a nervous start in the New Zealand capital, Ernie Merrick's men blitzed City to move six points clear of the Melbourne-based side.
Just two minutes into the second period and Burns showed real poise in the box to extend Wellington's lead further, while a Roy Krishna bullet in the 50th minute effectively ended the contest.
The goals took Burns to the top of the A-League goal-scoring charts with seven, two ahead of Melbourne Victory's Besart Berisha and Andy Keogh of Perth Glory.
Edson Montano's scrappy effort early in the second half had the Jets set for their first league win of the campaign.
However, Richard Vernes got ahead of his marker to convert Michael Neill's cross and snatch a point which does little to kick-start the Mariners' season in truth.
