Davis completed 26 of 40 passes for 264 yards and was the top rusher, with 63 yards on 15 carries, for Tennessee Tech (2-2).
Jordan Smith caught both of Davis' touchdown passes, Willie Davis ran in a TD from the 1 and John Arnold's 31-yard fourth quarter field goal gave Tennessee Tech the winning margin. Brock McCoin had 14 catches for 108 yards.
Murray State (1-3) closed the gap in the second half with a field goal and a pair of touchdowns, but the Racers had a PAT kick blocked and their 2-point conversion attempt that would have tied the game with 1:51 to play was stopped short.
KeDarius Humphries threw for 491 yards and three touchdowns.
AP College Football website: www.collegefootball.ap.org