Smith was the favorite target of quarterback Mason Mills, who completed 17 of 27 passes for 240 yards and three touchdowns.
San Diego (5-6, 5-3 Pioneer League), scored 15 points in the final quarter to rally for the win. Phil Morelli scored on a 4-yard run with 13 minutes to play, then Mills connected with Smith on a 27-yard touchdown pass play with 4:10 remaining to put the game away.
The Toreros' defense held Davidson to minus-10 yards rushing and sacked quarterback Jonathan Carkhuff eight times.
Davidson (3-7, 3-5) built a 15-14 lead after three quarters on the strength of two touchdown passes by Carkhuff, who was 16-of-27 for 258 yards.