The IBF champion came into the fight as the underdog but made a good start in round one, landing with some decent combinations.
However, the German responded well in the second, and Geale suffered a cut behind his left ear.
It was proving to be a very evenly-matched contest and the fighters were exchanging rounds.
The decision looked like it was going to be a close one, but two judges scored the bout 116-112 to the Australian.
The other judge scored it the same way, but in Sturm's favour.