Augsburg were the first to get a shot on target in the third minute, but Marcel de Jong put his effort wide of goal.
Then Diouf rose from a corner after 15 minutes but he could only find the stands.
Ten minutes later Diouf did have his goal, however, when he latched on to Lars Stindl's pass and found the net.
Hannover continued to dominate the half and but for an alert block Konstantin Rausch might have doubled the lead just a minute before the break.
In the second half Hannover remained on top, with Diouf shooting wide after 65 minutes and Dider Ya Konan having a shot well blocked five minutes later.
Just five minutes from time, Stindl made it 2-0 to the home side and wrapped up the points.