Bunting got off to an excellent start to the match at the Bahrain International Circuit and took the first leg from Price - even though the Welshman was unable to take out 170 after nine darts.
Bunting remained in control and increased his lead three times with further breaks, although he conceded a direct re-break after two of them.
The victory marks Bunting's first World Series win of his career and his first World Series event in 11 years.
In the quarter-finals, Bunting threw a 111.33 average in his 6-0 win over Chris Dobey, setting a tournament record, only for Price to break it in the next match with 115.31 in his 6-2 win over reigning champion Luke Littler.
Bunting also eliminated Luke Humphries earlier in his run to the final.
"It is even more satisfying because what an absolutely lovely trophy this is," Bunting told ITV after the win.
"I can't produce my best darts without this wonderful crowd week in, week out.
"The fanbase we are building at the moment is crazy. Thank you very much.
"I am lost for words. I am playing the best I have ever played, I am more consistent.
"Being world number five is an incredible feeling, and it has made me very strong, to be honest."
Nebrida shocks Cross
The biggest surprise of the tournament came on Thursday evening with Paolo Nebrida from the Philippines.
The World Championship participant met former world champion Rob Cross in the first round and won the match surprisingly easily by a score of 6-3.
The Englishman had to blame himself for the defeat: 'Voltage' hit only 13.6 per cent of his doubles with an average of 86.3. Nebrida was finally eliminated in the quarter-finals by Peter Wright.