In a tense finish at Le Golf National south of Paris, Ko held off a late charge from Germany's Esther Henseleit, who claimed silver two strokes behind the New Zealander.
China's Lin Xiyu was a further shot back to take bronze.
Ko, who started the final round as co-leader with Morgane Metraux of Switzerland, was cruising towards victory as she advanced to 11 under after her front nine holes to establish a five-stroke lead over Henseleit.
But a wayward shot on the 13th saw her hit the water en route to a double bogey, opening the door to Henseleit who cut Ko's lead to as little as one stroke.
Playing in the final group, two-time major winner and former world number one Ko kept her nerve with a string of par putts before slotting in a birdie on the 18th green to bag gold.
Gold for South Korean-born Ko will also bring her the remaining point she needed to enter the women's golf LPGA Hall of Fame.
Metraux slumped from her overnight co-lead to tied 18th at two under par, failing to recover from two bogies and a triple bogey in her first five holes.
Finishing on the same score as Metraux was France's Celine Boutier, who had thrilled home fans by taking a first-round lead on Wednesday.
Playing alongside Boutier, defending champion and world number one Nelly Korda of the United States fell out of medal contention during the final round to end at one under par in tied 22nd position.
