Dodd and Howell finished regulation tied atop the leaderboard at 9-under-par 279 after both players birdied the 72nd hole. They returned to the par-5 18th to begin the extra session and Howell split the fairway, while Dodd left his drive in the right rough.
Howell was unlucky with his approach, however, and sent his second shot into the rough to the right of the green. Dodd reached the putting surface with his second shot and two-putted for the win.
'Obviously I didn't expect to win twice in the starts that I've had,' said Dodd. 'But at the same time, I've put a lot of hard work in the last couple of years, and I feel like the work I've put in has finally paid off.'
Dodd held the 36-hole lead at Carton House Golf Club, but a 72 on Saturday left him four shots off the pace of Nick Dougherty heading into the final round. Dodd had a solid front nine with three birdies and a bogey before a birdie at the par-3 12th gave him a share of the lead at 8 under.
He added a birdie at the par-5 15th to move to minus-9, but stumbled to a bogey at the 17th. Dodd then birdied the closing hole to take the lead in the clubhouse after a round of 68.
Howell took the lead with a birdie at the ninth, but fell one back with a bogey at the 11th. Howell, who lost the Dunlop Masters in a playoff last week, found further trouble with a double bogey at the 14th.
The Englishman recovered in style with an eagle at the par-5 15th and closed with a birdie at the last for a round of 70 to join Dodd in the lead.
'Last week, I was gutted after losing the playoff, but today I wasn't,' Howell said. 'I was really pleased with how I finished. I drove it terribly today. I was laughing, really. I couldn't do anything but keep trying, and to get in the playoff I didn't surprise myself, but I'm proud of myself for doing it the way I drove the ball.'
Dougherty struggled to a 74 on Sunday to share third place with Angel Cabrera at 7-under-par 281. Padraig Harrington posted a 69 to finish one shot further back at 6-under-par 282 along with Lee Westwood and Nick O'Hern.
Francois Delamontagne finished alone in eighth place at 5-under-par 283. Richard Sterne, Oliver Wilson, Philip Golding and Steven O'Hara followed at 4-under-par 284.
Simon Dyson, Jose-Filipe Lima, David Carter and Colm Moriarty finished at 3-under-par 285. Darren Clarke was next at 2-under-par 286.