Shaw came out of the game late in the first half after re-injuring the same shoulder that forced him to miss last week's game.
That opened the door for Thompson, who completed 5-of-10 passes for 177 yards for the Gamecocks (3-0).
Shaw had hurled one TD pass with an interception before exiting.
The Blazers (0-2) were led by Jonathan Perry, who completed 17-of-34 passes for 219 yards.
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