Burns, who announced the end of his professional career on Friday, played a pivotal role as a dominant Glory put a huge dent in Central Coast's bid to shore up second spot on the A-League table.
Both teams converted penalties in the first half before Glory took control of the game to move off the bottom of the table with one round remaining.
Brazilian winger Sidnei was scintillating in the second half, scoring a goal and having a hand in another as Glory recorded their second victory from as many matches following a previous 10-game winless run.
Central Coast would have moved three points clear of Western Sydney with a win and now find themselves in third spot ahead of next weekend's clash with premiers Brisbane Roar.
Referee Stephen Lucas was kept busy in his first A-League match in charge, dishing out five yellow cards and awarding two penalties.
Chris Harold almost scored from an attempted cross in the sixth minute, but Mariners custodian Liam Reddy did well to keep the ball out.
Reddy's deflection veered into the path of Burns, who was brought down by Central Coast captain John Hutchinson on the edge of the six-yard box.
An unhappy Hutchinson, playing his 200th A-League match, argued with Lucas for almost a minute over the decision before being shown a yellow card for dissent.
Glory veteran Steven McGarry then stepped up to the spot and slotted the ball into the bottom left corner of the net to give Kenny Lowe's side an unlikely lead.
McGarry had a chance to score a second goal just five minutes later, but his long-range shot was just wide of the left post.
Burns then went from hero to villain when he brought down the speedy Kim Seung-Yong as the Korean attacker charged towards goal.
Nick Fitzgerald made no mistake from the spot to bring the Mariners back level after 19 minutes.
Mariners pair Eddy Bosnar and Matt Simon both found themselves in the referee's book for overzealous challenges as Glory finished the half as the dominant side.
Central Coast suffered a blow just before half-time when Kim was forced from the pitch with a leg injury.
Glory continued to control the game after the break, with wingers Harold and Sidnei both going agonisingly close to regaining the lead for their side.
Sidnei's attacking runs, in particular, caused plenty of headaches for the Mariners defence as they struggled to contain the Brazilian ace during the second half.
Impressive youngster Mitchell Duke was introduced just before the hour mark and came on with immediate impact, narrowly missing a header that would have put the Mariners in front.
However, Sidnei sealed Central Coast's fate when he volleyed a cross from teammate Nebojsa Marinkovic into the back of the net in the 71st minute to help Glory to just their seventh win of the season.
The night went from bad to worse for the Mariners when defender Zac Anderson scored an own goal as he attempted to thwart Sidnei's run.
Assistant referee Michael Jasinski raised his flag for offside, but he was over-ruled by Lucas and Glory's lead became insurmountable.
Mariners substitute Bernie Ibini appeared to grab one back for his side in injury time, but was ruled offside.
Perth Glory 3 (McGarry 8' pen, Sidnei 71', Anderson 85' og)
Central Coast 1 (Fitzgerald 19' pen)
Crowd: 11,127 at nib Stadium
