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Storm, whose ace came on the par three 11th, looked set for a share of the overnight lead until Brooks Koepka double bogeyed the last to drop back to 14 under.
Storm holed out with a six iron at Crans-sur-Sierre on his way to his second six-under par round of 64 and a one-shot lead over fellow Englishman Tommy Fleetwood.
"It was an incredible feeling," said Storm, ranked 159th in The Race to Dubai, after winning a BMW sports car worth around $163 000.
"I had a hole in one earlier in the season in Morocco and won a lamp, so I think this prize just about tops that one.
"To win a car is absolutely magnificent, especially as I had to sell mine because we couldn't afford to have two cars any more."
Storm won the French Open in 2007 but has missed the cut 14 times in 23 events this season.
Fleetwood carded a superb 63 featuring eight birdies and one bogey to finish 15 under par, one shot ahead of American Koepka who had shared the lead with Storm until finding water on the last to run up a double bogey.
Welshman Jamie Donaldson, looking for back-to-back wins after the Czech Masters, held a two-shot lead after four birdies in his first six holes but ran up a triple bogey on the 12th and double bogey on the 14th.
Birdies on the 13th and 15th limited the damage but a third round of 69 left the Ryder Cup player three off the lead on 12 under par alongside halfway leader Richie Ramsay and England's Tyrrell Hatton.
Ramsay, winner here in 2012, got off to a nightmare start with three bogeys in the first four holes but battled back to record a level-par 70, while Hatton had eagles on the first and ninth in his 65.
Ireland's Peter Lawrie had threatened to record the first ever 59 on the European Tour before being forced to settle for a round of 62.
Lee Slattery then threatened the magic number when he played his first 10 holes in seven under, only to find water off the tee and then three-putt the 13th for a triple-bogey six on his way to a 65.
Third round scores from the European Tour's European Masters at the par-70 Crans Montana course on Saturday (GBR & IRL unless stated):194 - Graeme Storm 64-66-64
195 - Tommy Fleetwood 64-68-63
196 - Brooks Koepka (USA) 65-65-66
197 - David Lipsky (USA) 67-64-66
198 - Tyrrell Hatton 67-66-65, Richie Ramsay 62-66-70, Jamie Donaldson 65-64-69
199 - Shane Lowry 66-65-68
200 - Victor Dubuisson (FRA) 65-67-68, Marco Crespi (ITA) 69-69-62, Gareth Maybin 64-67-69, Edoardo Molinari (ITA) 62-70-68
201 - Danny Willett 67-70-64, Peter Lawrie 69-70-62, Lee Slattery 68-68-65
202 - Romain Wattel (FRA) 68-69-65, Richard Green (AUS) 71-64-67, David Lynn 65-68-69, Seve Benson 65-67-70, James Morrison 66-69-67, Jyoti Randhawa (IND) 72-65-65
203 - Emiliano Grillo (ARG) 66-68-69, Marc Warren 69-63-71, Peter Whiteford 68-65-70, Bernd Wiesberger (AUT) 66-70-67, Raphael Jacquelin (FRA) 65-69-69, Julien Quesne (FRA) 69-66-68
204 - Robert Jan Derksen (NED) 66-67-71, Mikael Lundberg (SWE) 67-71-66, Mikko Ilonen (FIN) 73-66-65, Soren Hansen (DEN) 69-67-68, Nicolas Colsaerts (BEL) 68-67-69, Gary Stal (FRA) 71-66-67, Felipe Aguilar (CHI) 66-68-70, Joachim B Hansen (DEN) 72-67-65, Adrien Saddier (FRA) 69-67-68, Peter Uihlein (USA) 72-67-65, Wade Ormsby (AUS) 67-67-70, Mark Foster 69-68-67
205 - Craig Lee 66-70-69, Hennie Otto (RSA) 68-69-68, Matthew Nixon 66-69-70, Matteo Manassero (ITA) 68-71-66, Scott Jamieson 70-69-66, Brett Rumford (AUS) 69-65-71, Jamie McLeary 66-70-69, Thorbjorn Olesen (DEN) 69-69-67, Francois Calmels (FRA) 70-68-67, Adrian Otaegui (ESP) 68-70-67, Gregory Havret (FRA) 68-69-68, Anirban Lahiri (IND) 70-67-68
206 - Ricardo Gonzalez (ARG) 70-68-68, Thomas Bjorn (DEN) 66-72-68, Rikard Karlberg (SWE) 68-68-70, Nacho Elvira (ESP) 70-68-68, Morten Orum Madsen (DEN) 70-69-67, Michael Hoey 65-68-73, Alvaro Quiros (ESP) 69-68-69
207 - Richard Bland 70-69-68, Seuk-hyun Baek (KOR) 69-70-68, Anders Hansen (DEN) 67-71-69, David Howell 69-70-68, Martin Rominger (SUI) 68-70-69, Jason Knutzon (USA) 70-69-68, Peter Hanson (SWE) 66-68-73, David Drysdale 66-73-68, Paul Lawrie 70-68-69
208 - John Parry 71-68-69, Adilson Da Silva (BRA) 73-65-70, Matthew Baldwin 68-68- 72
209 - Sihwan Kim (KOR) 72-66-71, Robert Rock 69-69-71, Ricardo Santos (POR) 67-70-72, Chapchai Nirat (THA) 66-70-73, Padraig Harrington 66-71-72, Bradley Dredge 70-69-70
210 - Rahil Gangjee (IND) 72-67-71, Prom Meesawat (THA) 66-73-71
211 - Jose-Filipe Lima (POR) 71-68-72, Justin Walters (RSA) 70-68-73
213 - Johan Carlsson (SWE) 70-69-74
216 - Jin Jeong (KOR) 71-68-77
