Having led by two strokes after both the first and second rounds, Walker shot 69, 72 and 72 in the three-round event to tie with Campbell and Jorgensen on 213, six-under-par. The 27-year-old from Glasgow then sealed the wire-to-wire win by holing a birdie putt of 20 feet on the second extra hole, the 506-yard par-5 18th, playing over water.
"Amazing; absolutely brilliant. I'm delighted," said Walker. "I've been in play-offs to get in the British Open and US Open but not to win on the LET. I was just really trying to win and I kept giving myself chances and not quite making the putts, although I did putt quite well. A lot of them looked good and didn't go in, so I'm delighted to win in the end."
On the second play-off hole, Jorgensen made par before Walker perfectly judged her birdie putt. "With the crowd erupting it almost overwhelmed me, with everyone screaming," said Walker, whose previous best finish in five years on the LET was a tie for fourth at the 2011 Prague Masters.
Walker had a chance to win in regulation play after reaching the 18th green in two shots but three putted from across the green.
Her second round began well when she made a birdie putt of 15 feet on the second hole, but she dropped a shot on the par-5 third, before making her second birdie of the day on the seventh. From there she came home with 11 straight steady pars.
Earlier in the day, Campbell fired five birdies in her first eight holes and overtook Walker with her birdie on the sixth before picking up another shot on the par-5 eighth. However the 33-year-old Australian three-putted on 15 to drop back into a share of the lead.
Denmark's Jorgensen set the clubhouse target after firing a flawless six-under 67 in warm and sunny conditions and after ending second in Turkey, she finished runner-up for the second LET event in a row.
Kylie Walker won with a birdie on the second play-off hole
213 - Malene Jorgensen (DEN) 74 72 67, Kylie Walker (SCO) 69 72 72, Nikki Campbell (AUS) 72 72 69
215 - Camilla Lennarth (SWE) 75 69 71, Christel Boeljon (NED) 77 69 69
216 - Linda Wessberg (SWE) 73 73 70, Titiya Plucksataporn (THA) 73 70 73, Nontaya Srisawang (THA) 72 74 70
217 - Vikki Laing (SCO) 71 77 69, Krista Bakker (FIN) 72 74 71, Maria Balikoeva (RUS) 71 73 73
218 - Kim Williams (RSA) 75 69 74