Wallace led the Spaniard by four shots overnight, but shot a final round 70 to leave the pair all square at 11 under par.
Wallace held his nerve, claiming the title at the first sudden-death hole, the par-four 18th, with a birdie.
His last win on the Europe-based DP World Tour came six years in Denmark.
In third, a shot behind the play-off protagonists, came another English player, Andrew Johnston, with home Swiss hope Cedric Gugler and Australian Jason Scrivener in a tie for fourth, two shots further back.