Bourdy used the late surge to complete a round of 4-under-par 67 and finish at 8-under 276, two better than third-round leader Peter Uihlein.
The Frenchman thus earned his fourth career victory on the European Tour.
Uihlein was hoping to force a playoff by sinking a long birdie putt try on the 18th hole, but instead settled for a 1-over 72 and sole possession of second place at minus-6.
Ending one stroke further back was Soren Kjeldsen, who fired a 5-under 66 for the low round of the day and a third-place finish.
Celebrity Families of 2014 [PHOTOS]