The match contained few breaks of note - and no centuries - but Bingham came through in the deciding frame to receive the inaugural Ray Reardon Trophy from the six-time world champion himself.
Bingham, who had won his semi-final against Robert Milkins 6-0, carried on where he left off and roared into a 4-0 advantage against Trump, the highlight a cushion-first pot with swerve on the last red to help clinch the fourth.
He led 5-2 after a break of 87 but a double on the pink narrowly stayed out to allow Trump to snatch the final frame of the session.
The first two frames of the evening were shared before Trump won two in a row, including frame 12 with the help of three doubles and a superb snooker on the yellow.
Again the players traded frames and a close-run 17th frame followed, the tension ramped up by the knowledge whoever won the frame would move within one of victory.
A fine cut on the green allowed Trump to take the frame with a testing clearance to the pink, his fist-pump reflecting the significance of the moment, but the Bristolian shockingly missed a red along the top cushion when in position to win the match and, after another lengthy tussle on the colours, Bingham forced a decider.
An aggressive safety from Trump opened the reds up but he was punished when Bingham rattled in a long red and cleared to the pink to win frame and match.
An emotional Bingham said afterwards: "It's unbelievable. I thought it wasn't going to be my day.
"From 4-0 down a lot of people would have crumbled but credit to Judd, he took the game to me and I thought he outclassed me in every department."
Bingham's second child, daughter Marnie, was born last month and he said: "She's here as well somewhere, the wife said she wouldn't be able to come up so it was a great surprise.
"And with this new Ray Reardon Trophy - he's a living legend, we haven't got that many six-time world champions, so I'm honoured to be getting the trophy off him."
