Poole went 6-of-8 from beyond the arc and dished off four assists. Isaiah Canaan added 15 points and seven assists for the Racers (10-0), who led most of the second half but had to hang on at the end.
Canaan hit two foul shots with 8 seconds remaining and the Tigers' Chris Crawford missed a potential score-tying 3-pointer on the next possession, icing the upset for Murray State.
The Racers finished 9-of-20 from 3-point range.
The Tigers (5-3), meanwhile, had their three-game winning streak snapped despite a game-high 27 points from Will Barton and Joe Jackson's 20.