Both players finished 72 holes at Castle Stuart Golf Links at 17-under 271 -- Singh fired a 5-under 67 to charge from behind while Molinari hung in with a round of even-par 72.
The competitors returned to the 18th hole for the playoff, during which Molinari put his second shot 25 feet from the pin and Singh got to within 15 feet.
Molinari's birdie effort was well short but Singh followed with a putt into the middle of the cup for his fourth career European Tour win.
The victory enabled him to claim one of the final spots in the field for next week's British Open.
Marc Warren held a brief lead Sunday but double-bogeyed the 15th and followed with bogeys on 16 and 17 to finish with a round of 1-under 71, sharing third place with Alexander Noren (70) at 16-under 272.