In just his third start of a campaign beset by a lingering groin injury, Burgess grabbed a second-half double after setting up Patrick Wood for the game's opening goal with a sumptuous through ball.
English winger Joe Lolley grabbed Sydney's other goal at Allianz Stadium on Friday as Ufuk Talay's men condemned the Jets to their biggest defeat of the season.
Sydney move up to fifth on the ladder, while Newcastle are languishing in 10th after one win in their last six games.
Bondi blue: Joe Lolley celebrated his new two-year contract with a goal in Sydney's 4-0 win. (Flavio Brancaleone/AAP PHOTOS)
The Jets caught Sydney off guard in the early stages when Apostolos Stamatelopoulos latched onto a long ball forward from left-back Daniel Wilmering after just eight minutes.
Stamatelopoulos bore down on goal and finished past Andrew Redmayne but a VAR check revealed the Jets frontman was marginally offside and the goal was chalked off.
Sydney breathed a sigh of relief and began to turn the tables as they put the Jets under increasing pressure.
Jordan Courtney-Perkins fired a close-range header straight at Ryan Scott with the Newcastle goalkeeper also palming away a 30-metre rocket from Luke Brattan.
Newcastle's resistance finally wavered in the 40th minute, with Burgess able to slip Wood in behind the Jets' defence.
The striker found the back of the net with a well-executed chip over the on-rushing Scott to give Sydney a 1-0 lead at halftime.
The Sky Blues were in the mood for more, with Wood having an effort chalked off for offside and Gabriel Lacerda forcing Scott into action once again.
Newcastle had the odd half-chance but Sydney made the majority of the running and Lolley made it count by extending their lead in the 66th minute.
Lolley, who signed a two-year contract extension earlier this week, cut in off his wing, drove into the Jets box and blasted the ball past Scott.
Wood was subbed off for Fabio Gomes soon after and the Brazilian wasted no time getting in on the act, flashing a cross to the back post where Burgess headed in.
Newcastle's heads dropped and Burgess was able add his second - and Sydney's fourth - burying a low shot past Scott to wrap things up with 10 minutes left.
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