The 27-year-old from Glasgow had led by two shots heading into the final round but a one-under 72 allowed Denmark's Malene Jorgensen and Australian Nikki Campbell to catch her.
Jorgensen set the clubhouse lead on 213, six under par, after shooting a 67, and although Campbell led for much of the day after five birdies in her opening eight holes, she three-putted the par-5 15th to drop back into a tie with Jorgensen and was later joined by Walker.
The Scot had the chance to win in regulation after reaching the 507-yard last in two, but she then three-putted for par to go into the three-way play-off. The first hole was halved, but Walker finally secured victory on the second extra hole, sinking a 20-foot birdie putt at the par-5 18th to take the title and the €37,000 first prize
"Amazing, absolutely brilliant, I'm delighted," said Walker. "I've been in play-offs to get into the British Open and US Open but not to win on the LET. 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."
Vikki Laing, from Musselburgh, shared ninth place on 217.
In Alabama, Catriona Matthew just failed to catch America's Jessica Korda in the final round of the Airbus LPGA Classic at Mobile. Korda reached the turn in 35, then came home in 30 for a 65 and a winning aggregate of 268, 20 under par.
Matthew reached the turn in 34, two under, with birdies at the third, sixth and ninth offset by a bogey at the seventh. However, bogeys at the 10th and 12th saw her drop back, but the Scot never stops trying and she responded with birdies at 13, 14 and 16. She then parred the last two holes to finish in a tie for third on 270, one shot behind Anna Nordqvist, of Sweden, and alongside America's Michelle Wie and England's Charley Hull.