After a tight first set, Babos took control with a hard-hitting display to claim her third WTA singles trophy of her career.
After dropping the first set, Kozlova, 23, had a misstep serving at 1-0 in the second set, when she hit two unforced errors and a double fault to be broken right away. Babos pounced, holding serve for a commanding 3-0 lead.
Kozlova won the next game but Babos held to go up 4-1 and broke her opponent again before serving for the win.
Kozlova, contesting her first WTA final, had beaten Babos in their only previous meeting, in the qualifying of the 2015 Qatar Total Open in Doha.
Babos added to previous title runs at the Abierto GNP Seguros in Monterrey in 2012 and the Hungarian Ladies Open in Budapest last year.