Wesley Clemmons made a 3-pointer with just over a minute remaining to give the Salukis a 55-52 lead but Mike Green converted a layup for the Bulldogs.
Southern Illinois' Tyrone Green then missed a free throw, setting the stage for Graves' shot.
Mike Green led Butler (12-1) with 19 points. Matt Howard added 15 and Graves finished with 10.
Joshua Bone scored a career-high 19 points, including five 3-pointers, for the Salukis (5-6). Randal Falker added 14 points.
Matt Shaw, Southern Illinois' leading scorer, was held without a basket. He went 0-for-7 from the field and missed both of his free-throw attempts.
Butler survived a nearly 14-minute span in the second half without recording a field goal. The Bulldogs went 12-for-18 from the free-throw line after halftime and made 21 of 30 free throws for the game.
Butler put together an 8-0 run late in the first half and led 31-29 at halftime.
