Trailing Brett Rumford by two strokes late in the match, Moinari staged a stunning comeback with three straight birdies to post his second win of the season in Scotland -- he earlier took the Scottish Open.
Molinari fired a 1-under 71 to end at 10-under-par 278 while Rumford birdied the final two holes to end at 2-under 70, taking second place at minus-9.
Third-round leader Francesco Molinari dipped to a 75, ending in a third-place tie with Miguel Angel Jimenez (72) and Jamie Donaldson (69) at minus-7.
Simon Dyson ended sixth at minus-6.
After Sunday's round, Ryder Cup captain Colin Montgomerie chose Edoardo Molinari along with Padraig Harrington and Luke Donald for the European team.