Bunting was bottom of the Premier League table without a single win leading up to night nine but edged past Gerwyn Price 6-5 in a thrilling finale.
The 39-year-old lost his opening three throws but held his nerve to win the last two legs and earn his first points of the campaign.
"This is such a special moment," he told Sky Sports. "There have been times during the Premier League where I've thought, 'could I finish on zero points'?
"To get off the mark tonight and win a night, it's such a special feeling.
"It was a monkey on my back, the first game. I'd felt so good in the practice room - I hit a nine-darter - and that gave me a lot of confidence."
Bunting reached the final after beating Nathan Aspinall 6-2 in the opening match of the night, before brushing aside world number one Luke Humphries by the same score in the semi-final - to record only his second victory in eight weeks.
Earlier, reigning champion Luke Littler was stunned by Chris Dobey in one of the biggest shocks of the Premier League so far.
The 18-year-old, who was looking to become the first player in history to win five nightly wins in the same season, led 1-0 in their quarter-final clash but then lost five legs on the bounce.
Despite pulling the score back to 5-2, Dobey held his nerve and throw to take his sixth and decisive leg.
"It was an uncharacteristic performance from Luke," Sky Sports' Mark Webster said. "He looked disappointed at the end - he just left himself with too much work to do.
"A big win for Dobey and a good boost for the other players too."
Michael van Gerwen withdrew from the competition with a shoulder injury allowing Gerwyn Price a bye to the semi-finals, and the Welshman reached the final with a 6-2 win over Dobey.