Rybakina came back from a break down in both sets and also saved set points in each to overcome the eighth seeded Croatian in a little over two hours for her 19th victory of the year.
Brady, playing for a seventh straight day having got through three qualifiers, made 14 unforced errors to give the Wimbledon champion a chance to win her first trophy of the year.
"First set it was not easy because she (Martic) plays really good," Rybakina said. "She has really good slices.
"Her serve, it's not flat like I played with Pliskova, for example. It's a completely different style of game. It was not easy to start against her.
"But I tried to work every point. Second set, I was 3-0 down but I knew it was going to be easier to win this set than play a third one. I wanted to win the second so much."
Rybakina fired down six aces and 32 winners, many from her powerful forehand that had Martic chasing her returns in vain.