Di Santo finally made the breakthrough in the 43rd minute with a brilliant effort from a difficult angle over Kraft and in off the far post.
The Argentine sealed the result with a mishit volley from Clemens Fritz' cross that bounced beyond the helpless Kraft in the 69th.
Bremen moved two points clear of Hertha, which is just one point above the relegation places.
Augsburg was hosting Hoffenheim later with both sides hoping to secure European qualification.
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