Carr completed 33-for-46 passes for 412 yards while Adams made eight catches for 221 yards as the Bulldogs (6-0, 3-0 MWC) equaled the best start in school history.
The last time they began a season at 6-0 was in 2001 when Carr's brother David was behind center.
The Rebels (4-3, 2-1) had a four-game winning streak snapped.
Caleb Herring was limited to 161 yards with a touchdown on 27-of-42 efficiency. Shaquille Murray-Lawrence gained 79 yards and scored a touchdown on three carries for UNLV.