The Miners (4-5, 2-3 Conference USA) marched 73 yards in 16 plays, chewing up 7:25, for the winning field goal. Leftwich twice connected with Hayden Pinke, for gains of 8 and 11 yards, to keep the drive alive.
The Miners knocked down a desperation pass in the end zone on the final play.
Rice (4-5, 2-3) scored twice in the second quarter, a 3-yard run by Luke Turner and a 36-yard pass from Driphus Jackson to Zach Wright, but Leftwich countered with 58- and 2-yard TD hookups with White.
Jeremiah Laufasa's 2-yard run put the Miners on top in the third quarter before Jackson hit Luke Turner for a 23-yard score to tie it again.