Taliah Scott led all scorers with 25 points in front of 11,026 spectators as the Racers made a furious late charge to try and steal one at the end.
The Razorbacks (2-0) led by 16 at intermission and held their biggest lead at 24 midway through the third quarter, but Murray State kept chipping away.
Murray State outrebounded the Hogs 48-42 and shot 35 percent from behind the 3-point line, making 11 of 32.
Arkansas overcame 18 turnovers and poor perimeter shooting, as it made only 7 of 25 treys.
Saylor Poffenbarger had a double-double with 10 points and 12 rebounds. Sasha Goforth added nine points and three blocks off the bench.