The Bristolian was in brilliant form throughout Sundays final stages, hitting a total of 16 maximum 180's, including ten in a thrilling semi-final against Ronnie Baxter.
He overcame James Wade 5-4 in their quarter-final clash, hitting an 87 checkout in the deciding leg, before being pushed all the way by Baxter.
Dudbridge led by a set but saw Baxter - who has recently moved to Swindon - hit back to level matters after he missed a dart for the game.
Dudbridge led 2-0 in the final set and, although he was pegged back to 202, he regained his composure to move into the final.
Priestley took the opening leg of the final with a 106 finish, but Dudbridge responded with three straight legs to take the opening set.
A 12-dart leg from Priestley again saw him lead in the second, but he paid for missed doubles in the next two as Dudbridge moved close to victory.
He then secured the £4,000 winner's cheque, landing another 180 to surge clear in the fourth leg and then double 18 for the title.
"I'm very pleased," said a delighted Dudbridge. "It's been a rocky road and I've found it difficult for the last year because there's been a lot of pressure on me.
"People expect things of me now and I've pulled it off this weekend. I've had some tough games this weekend, Keith Rooney had a dart to beat me on Saturday so things could have been different.
"Things seem to be coming together for me now and it's a big boost."
Priestley, who won the Stan James Players Championship in Gibraltar last month, saw his fine form continue in Swindon.
After defeating Phil Taylor and Keith Deller on Saturday, he then overcame Robbie Widdows and Adrian Lewis to reach another final.
Budweiser UK Open South-West Regional Final
Quarter-Finals
Adrian Lewis 5-1 Darren Latham
Robbie Widdows 1-5 Dennis Priestley
Ronnie Baxter 5-2 Andy Jenkins
James Wade 4-5 Mark Dudbridge
Best of nine legs
Losers £500/10 ranking points
Semi-Finals
Adrian Lewis 0-2 Dennis Priestley (1-3, 2-3)
Ronnie Baxter 1-2 Mark Dudbridge (1-3, 3-2, 2-3)
Best of three sets, five legs per set
Losers £1,000/12 ranking points
Final
Dennis Priestley 0-2 Mark Dudbridge (1-3, 1-3)
Best of three sets, five legs per set
Winner £4,000/20 ranking points
Runner-up £2,000/16 ranking points
Click here for Day One Results & Round-up
QUARTER-FINALS
ADRIAN LEWIS 5-1 DARREN LATHAM
ADRIAN LEWIS moved into semi-finals with a 5-1 win over Darren Latham.
Latham, who overcame John Part and Colin Lloyd on Saturday to reach the last eight, paid for missed doubles in the first two legs.
Lewis stepped in to move into a 2-0 lead, with Latham hitting back to win the third by landing double top.
Lewis, though, took the next three legs without reply to remain on course for a second Regional Final win of the tournament - having also taken victory in Scotland last November.
DENNIS PRIESTLEY 5-1 ROBBIE WIDDOWS
DENNIS PRIESTLEY showed all his class to defeat Robbie Widdows and move into the semi-finals.
The Yorkshireman won the opening leg, although he was pegged back when Widdows landed a brilliant 136 checkout.
Priestley regained the lead with a 12-dart leg and reeled off three more to ensure his place in the last four.
RONNIE BAXTER 5-2 ANDY JENKINS
RONNIE BAXTER came from behind to defeat Andy Jenkins 5-2 in the third quarter-final clash.
Baxter trailed 2-1 after Jenkins held his throw in the opening three legs.
However, the newly-based Swindon star found top gear to win four straight legs - including a 117 finish - and book his semi-final berth.
MARK DUDBRIDGE 5-4 JAMES WADE
MARK DUDBRIDGE edged out James Wade in a tense deciding leg to reach the last four of the South-West Regional Final.
After winning the opening leg, Dudbridge found himself 3-1 down as Wade proved clinical in his finishing.
Dudbridge landed a maximum in the fifth leg before landing a 78 finish, but Wade eventually landed double five in the next to go 4-2 up.
Bristol star Dudbridge lifted his game to win the next three legs and wrap up the narrowest of wins.
SEMI FINALS
ADRIAN LEWIS 0-2 DENNIS PRIESTLEY
DENNIS PRIESTLEY defeated Adrian Lewis in straight sets to reach the final of the South-West Regional Final.
Lewis, the winner of the Scottish Regional Final in November, started strongly with a 13-dart leg, but Priestley's consistency saw him take three successive legs and the first set.
A 12-dart leg saw Lewis move in front in the next set, but Priestley hit back to level matters.
Stoke youngster Lewis moved 2-1 up in the set with a 14-dart leg, but was punished for two missed darts at double top as Priestley levelled the game and then took victory.
RONNIE BAXTER 1-2 MARK DUDBRIDGE
MARK DUDBRIDGE landed ten maximum 180's during his semi-final against Ronnie Baxter - but only moved into the final following a dramatic final leg shoot-out.
Baxter took the opening leg with a 76 finish, but Dudbridge opened the next three with 180's and took the first set 3-1.
He also hit three more maximums in taking a 2-1 lead in the second set, although Baxter managed to stay in the game by landing double eight.
Dudbridge missed double top for the match in the next leg, with Baxter landing double 17 to level matters at one set apiece.
Dudbridge moved 2-0 up in the decider before being pegged back to 2-2, with Baxter landing a two-dart 78 after seeing his opponent miss double four for victory.
However, Dudbridge landed a tenth maximum of the game in the sudden-death final leg and wrapped up his win in 11 darts.