Fleetwood's birdie on No. 18 gave him a round of 2-under 70, catching Ricardo Gonzalez (70) and Stephen Gallacher (67) at 18-under-par 270 on the PGA Centenary Course at Gleneagles.
That set up a three-way battle as the golfers returned to the par-five 18th for a playoff.
Fleetwood found the fringe with his second shot and had a chance to win it with a 22-foot eagle putt, but it went wide.
Gallacher and Gonzalez, however, each missed birdie putt attempts, while Fleetwood's short birdie try found the hole, giving the Briton his first European Tour title.
Sharing fourth place at minus-17 were Scott Henry (67) and Bernd Wiesberger (68).
Emiliano Grillo (66), Paul Waring (67) and Brett Rumford (68) knotted for sixth one shot further back.
Celebrity Families of 2014 [PHOTOS]