Dillard, who pushed his NCAA record for career touchdowns to 54, caught seven passes for 141 yards. The Owls (4-3, 3-1 Conference USA) moved to 3-0 at home and have won two of three after a two-game slide.
Southern Miss (2-5, 0-3) has lost four straight.
Davis was 32-of-61 for 461 yards and threw all four of his touchdown passes to Brown, who had 221 yards receiving. Damion Fletcher had a game-high 120 yards rushing on 17 carries.
After Clement hit Dillard for a 44-yard score to make it 38-26 with 11:45 left, Rice got its final touchdown when James Casey scooped up a fumble from teammate Patrick Randolph and ran it 26 yards to the end zone.
The Owls led 17-12 at halftime behind Clement, who finished the game completing 30 of his 43 passes.