Davis completed 23 of 30 passes for 285 yards without an interception, and rushed for 111 yards on 17 carries to give the Golden Eagles (8-3) an emotional win just six days after three players were shot outside a Hattiesburg nightclub.
One of those players, linebacker Martez Smith, made an appearance before the game to be honored on Senior Day.
Houston quarterback David Piland set the single-game passing record for M.M. Roberts Stadium with 467 yards and four touchdowns, but it didn't make up for an anemic rushing game that accounted for just 30 yards on 19 attempts.
Kendrick Hardy rushed for 205 yards on 26 carries for Southern Miss with two touchdowns.
Houston (5-6) fell to 4-4 in Conference USA and out of contention for the league's Western Division.