Robertson had looked on course for a straightforward victory after some excellent break building put him on the verge of a 4-2 win.
But under the pressure of the final he began to miss easy balls, and Burnett grabbed his opportunity to force a deciding frame.
"I thought it was going to be an early night, but then at 3-3 I was under pressure because I would have been devastated to lose, so I was just relieved to win in the end," said 2010 world champion Robertson.
The seventh frame started as a cagey affair which could easily have called for a re-rack, but the players stuck it out over 52 minutes as Robertson made it over the line to deny Burnett a first professional title.
"I won this tournament last season and went on to win another PTC event and then the Masters, so hopefully again this will be the start of a really good season for me," Robertson added.
"The crowd here was fantastic, the people really love snooker so it's great to come here and put on some world class snooker."
Robertson had made the final with a 4-2 win to stop Stephen Maguire's charging week at the semi-final stage, an impressive win considering that the Scot had lost just three frames in five matches.
Burnett qualified for the final in equally promising fashion, whitewashing Michael Holt 4-0 in the semis.
But with Burnett's early-round brilliance deserting him early on in the final and putting him on the back foot it was the Australian who pushed on to win.
The Players Tour Championship consists of 10 events - four in the UK and six in Europe - with the top 25 on the final Order of Merit going through to the Grand Finals in March.
They will be joined by seven players from the Asian PTC Order of Merit. The next event is the Antwerp Open in Belgium from October 18-21.
Neil Robertson 4-3 Jamie Burnett
Stephen Maguire 2-4 Neil Robertson
Michael Holt 0-4 Jamie Burnett
Stephen Maguire 4-1 Jimmy White
Michael Holt 4-2 Ding Junhui
Tian Pengfei 0-4 Neil Robertson
Jamie Burnett 4-3 Kurt Maflin