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The Hungarian fourth seed carried over the momentum from the Australian Open to win in straight sets, 7-5, 6-1.
It was her third WTA singles title after winning the Abierto GNP Seguros in Monterrey in 2012 and the Hungarian Ladies Open in Budapest last year.
Kozlova was making her debut at a WTA final. She stayed close in the first set but conceded an easy victory in the second.
The Ukrainian, ranked 85th in the world, had beaten Babos in their last encounter at the 2015 Qatar Total Open in Doha.
She had earlier knocked out fifth seed Yulia Putintseva of Kazakhstan and former Wimbledon finalist Sabine Lisicki of Germany in the semifinal before facing Babos.