Alastair Forsyth and Mark McNulty both fired rounds of 4-under 68 to finish in second place at 15-under-par 273.
Price was in control most of the day until a three-putt bogey on 17 on the North Course at The Kildare Hotel & Country Club dropped him into a three-way tie for the lead with the par-5 18th to play.
He knocked his second shot on 18 just over the back edge before pitching to two feet. Price calmly drained the putt for birdie and the title.
'I was battling in the end,' said Price, a hero on the 2002 European Ryder Cup team. 'I played okay but it's tough when some of the other guys are playing well. I missed that short putt on 17 and thought I blew it, but to get up-and-down at the last was fantastic.'
Price, who had missed his last two cuts, entered the final round with a three- stroke lead. The advantage dipped to two shots when Darren Clarke birdied the second and McNulty birdied the third to both climb to 12-under.
The Welshman was briefly caught by Clarke, who hails from Northern Ireland. Clarke eagled the par-5 fourth to join Price at 14-under, but Price birdied the fourth to regain the lead.
Clarke dropped off the pace with back-to-back bogeys from the sixth. Price then rolled home a birdie try on the eighth to extend his lead to two strokes.
McNulty birdied No. 10 to get within one. Price, however, birdied the same hole to push his lead back to two shots.
Price's lead grew to three shots after he holed out for birdie at the par-3 12th. His tee ball had found the greenside bunker, but he managed to blast out and roll his ball into the cup.
He stumbled to a bogey at the par-3 14th when his tee shot missed the green and he hit a poor chip before two-putting. Price parred the next two holes after his tee shot on both holes found the rough.
Price knocked his drive into the first cut of rough off the 17th tee. His second found the green, but he missed a short par-saving putt to set up the late dramatics.
'If I had holed my putt for par on the 17th I probably could have coasted down the last, but I left myself a bit of work to do,' Price said. 'I was hoping I would hit the chip stiff but I hit it to two feet which was pretty good and it was a relief to see the putt go into the middle of the hole.'
The win for Price was the sixth wire-to-wire victory on tour this season. It is also the second title for a Welshman. Bradley Dredge won the Madeira Island Open earlier this season.
This represents the first time two Welsh golfers have won official events in the same season since 1994 when Price won the Algarve Open de Portugal and Ian Woosnam won the British Masters.
'I suppose I'm a bit short on titles and it has bothered me a little bit that I haven't won more often, especially a big tournament,' said Price, who picked up his third title on the European Tour. 'But I class this as a big tournament and to win here is just fantastic.'
Forsyth posted three birdies and a bogey on the front side before birdies on 16 and 18 moved him into a share of second.
McNulty had a steady round with back-to-back birdies from the third. He sank two more birdies around the turn for a bogey-free 68.
'I'm absolutely delighted with the week, thrilled,' said the 49-year-old McNulty. 'I think that is the best I have played for five years. To play on a tough, demanding golf course like this and only drop three shots all week, is a fantastic effort.'
Gary Evans finished alone in fourth place at 13-under-par 275. Eduardo Romero and Clarke were one shot further back at minus-12. Jarmo Sandelin and Andrew Coltart shared seventh place at 10-under-par 278.
Michael Campbell, the 2002 champion, struggled throughout the tournament and finished at 4-over-par 292 after a 5-over 77 on Sunday.