The victory was the Wolf Pack's first in its season opener since it beat Southern Utah, 24-23, in 2003.
Grambling State (0-1), which was out-gained 629-230, was led by quarterback Greg Dillon, who completed 13-of-25 passes for 225 yards. Dillon connected with running back Kenneth Batiste on a 21-yard touchdown pass to close out the scoring with 4:38 to play.
Kaepernick, who also completed 10-of-17 passes for 122 yards, scored on runs of 7 and 19 yards to open the scoring. The sophomore quarterback, who also scored on a 28-yard run in the third quarter, finished with 69 yards rushing on just six carries.
Nevada running back Vai Taua had a game-high 103 yards rushing on 12 carries. The sophomore scored on a 1-yard run in the second quarter as Nevada took a 21-0 halftime lead and added a 4-yard score in the third quarter.
The Nevada defense held Grambling State to minus 11 yards rushing in the first half and just 5 total yards on the ground for the game on 40 carries. Nevada's offense rushed for 426 yards on 53 carries. Four Wolf Pack quarterbacks combined to complete 18-of-32 passes for 203 yards.
Grambling State broke Nevada's shutout with 9:19 to play in the third quarter on a 61-yard interception return for a touchdown by Desmond Lenard.