Henin took advantage of some shaky play by the 19-year-old Serb, who was playing in her first Grand Slam final.
The Belgian trailed in each of the first four games, which took 24 minutes, but won 18 of the next 22 points.
Henin extended an Open era record winning streak of 35 consecutive sets at Roland Garros.
She's the first woman since Monica Seles in the early 1990s to win three consecutive Roland Garros titles, and only the second since 1937. And she's the fifth woman since 1925 to win the French Open four times. Chris Evert leads with seven titles.