The Serbian won the first set on a tie-break before breaking Federer twice in the remaining moments to claim the second set 7-5.
"This was a title for him. He's much better now. At a certain stage it was very critical. We didn't know what tomorrow brings, but now he's much better and he's recovering," Djokovic told reporters.
"He's still in intensive care. I'm going to visit him and see how it goes and try to bring the trophy with me and at least make him smile."
It is understood that his father Srdjan is suffering from an acute respiratory illness.