Bunting was bottom of the Premier League table without a single win leading up to night nine but stormed past Nathan Aspinall and Luke Humphries before edging past Gerwyn Price 6-5 in a thrilling finale.
The 39-year-old lost his opening three throws in the final but held his nerve to win a last-leg decider with a 107 checkout and collect his first five points of a bruising campaign.
"It's unbelievable, a pinch-me moment," he told Sky Sports. "I've tried 110 per cent every single week. You see some negative comments come through on social media, but I just try and stay away from them."
Bunting hit a nine-darter in practice and then beat Aspinall 6-2 in the opening match of the night with a 103.4 average, before brushing aside world number one Humphries by the same score in the semi-final to record only his second victory in eight weeks.
"This is such a special moment. 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."
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 on to become the first player to beat the Warrington teenager by a four-leg margin this year.
"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.
The Premier League continues next Thursday, 10th April, in Manchester.