Australia's Robertson clearly enjoys playing in Poland as he has won the only two professional events to be staged in the country, having triumphed at the Warsaw Classic last season.
Victory for the Australian is worth 12,000 Euros plus 2,000 ranking points and a guaranteed place in the Players Tour Championship Grand Finals next March.
World No 8 Robertson reached the final of that event last season but lost to Stephen Lee - the only time he has ever come off second best in a televised final.
Masters champion Robertson had a slow start to the season but showed signs of his best form at the Hala Sportowo-Widowiskowa in Gdynia.
He appeared to be crusing to victory over World No 39 Burnett when he went 3-0 up with a top break of 118, but his opponennt, who was seeking his first pro title, battled back to 3-3 with a top run of 64.
The decider was a tense affair lasting 52 minutes, and Hamilton's Burnett had a chance to win it but missed a black off its spot with one red left, trailing by 30 points. Robertson seized his chance to secure the trophy.
"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.
"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.
"The crowd here was fantastic, the people really love snooker so it's great to come here and put on some world class snooker."
The Players Tour Championship is a series of 10 events, four in the UK and six on the Betfair European Tour, 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.